 Ratios and percent. It turns out the explicit formula for a geometric sequence is the formula below,  This is because when evaluating investment returns as annual percent change . , S n (the sum of the first n terms) is known in mathematics as a geometric series. 2. This can be seen easily from the fact that the sequences do converge to a common limit (which can be shown by  May 8, 2014 An Geometric Sequence describes something that is periodically growing in an exponential fashion (by the same percentage each time), and a  Percentages - geometric progression - solved math problems, problem solving and knowledge review. Insert one of the Formula to divide a lump sum by percentages . Geometric Sequence (Geometric Progression) In geometric sequences, also called geometric progressions, each term is calculated by multiplying the previous term by a constant. In a decreasing geometric sequence, the constant we multiply by is less than 1, e. Geometric sequence Before talking about geometric sequence, in math, a sequence is a set of numbers that follow a pattern. A geometric sequence or progression is a sequence of numbers in which each term after the first is found by multiplying the previous term by a fixed number, called the common ratio. The IRR function in Excel returns the internal rate of return for a series of  Percentage Rate (APR) prominently. When an asset loses value by an annual percentage, it is known as Declining Balance Depreciation. A geometric sequence is a sequence derived by multiplying the last term by a constant. In an Arithmetic Sequence the difference between one term and the next is a constant. Mathematicians calculate a term in the series by multiplying the initial value in the sequence by the rate raised to the power of one less than the term number. 1. As you work through it, you will discover that algebra and geometry have been . This video walks you through the steps of using geometric series sum to figure out mortgage payments. Geometric sequence worksheets are prepared for determining the geometric sequence, finding first term and common ratio, finding the n th term of a geometric sequence, finding next three terms of the sequence and much more. It is estimated that the student population will increase by 4% each year. Of all who embark on higher education, only 58 percent end up with  Jan 8, 2019 Data interpretation problems, for instance, can double as geometry and statistics GRE Quant Concept, Percentage frequency on the test If sequence or function problems appear on your exam at all, you'll likely have one  314 items Related Topics: fractals, fractions, geometric sequences, pattern, pre-calculus, geometric probability, outcomes, percentages, probability simulation,  Mar 14, 2018 Posted in Based on an ImageTagged A Level > Geometric sequences, Probability > Probability of a single event  Percentages and simple percentage problems would normally precede the unitary method approach to them. In this case, "small" means . . determine arithmetic and geometric series Solve word problems containing several rates, proportions, or percentages. Guidelines to use the calculator If you select a n, n is the nth term of the sequence If you select S n, n is the first n term of the sequence For more information on how to find the common difference or sum, see this lesson Geometric sequence a 1 is the first term of the sequence, n is the number of terms, d is the common difference, S n is the sum of the first n terms of the sequence. 4 Geometric series. Geometric Sequence Calculator Find indices, sums and common ratio of a geometric sequence step-by-step Geometric sequence question? with percents? Sam invested $5000 in a GIC earning 8% compound interest per year. . 2. Geometric sequences calculator that shows all the work, detailed explanation and steps. If your pre-calculus teacher gives you any two nonconsecutive terms of a geometric sequence, you can find the general formula of the sequence as well as any specified term. The geometric average is found by taking the individual percentages and When considering investment returns it is the geometric average, not arithmetic average, that matters. In this lesson, we focus on the geometric sequences from this activity. What is the percent increase from 700 to 2000 by using geometric sequence? Percentage change from V1 = 700 to V2 = 2000: [ ((V2 - V1) / |V1|) * 100 ] Geometric Sequence 3)Varied-formula Geometric sequences of numbers. When plotted in order, these numbers resemble more of a curve than a straight D. Then he explores equivalent forms the explicit formula and finds the corresponding recursive formula. Which explicit function represents the geometric sequence of the heights of the toy? Geometric Sequences Assignment study guide by akito-bloodless includes 8 questions covering vocabulary, terms and more. A bouncing toy reaches a height of 64 inches at its first peak, 48 inches at its second peak, and 36 inches at its third peak. 5. 1 Convert between percents, fractions, and decimals · D. So, if a decimal multiplier equivalent values, not percent values (i. Because a geometric sequence is an exponential function whose domain is the set of positive integers, and the common ratio is the base of the function, we can write explicit formulas that allow us to find particular terms. A Sequence is a set of things (usually numbers) that are in order. About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the Thus if you are starting out with a sum of money that is compounded for interest, then the mean that you should look for is the geometric mean. Some of the worksheets displayed are Geometric sequences date period, Arithmetic and geometric series work 1, Finite geometric series, 9 11 sequences word, Arithmetic and geometric sequences work, Arithmetic and geometric sequences and series, Sequences series This extensive collection of series and sequence worksheets is recommended for high school students. 1 - SERIES 1 - ELEMENTARY PROGRESSIONS AND SERIES 2. An infinite geometric sequence is a geometric sequence with an infinite number of terms. 5 Practice: Geometric Sequences Assume that the ball rebounds the same percentage on Write the explicit formula for the geometric sequence of the height In a previous post, I shared the definitions my class used for arithmetic and geometric sequences: An arithmetic sequence is a sequence for which the difference between consecutive terms is a constant, call the common difference. The common ratio is the number multiplied to get the next term. Note that after the first term, the next term is obtained by multiplying the preceding element by 3. Showing top 8 worksheets in the category - Geometric Sequence. Example: An investor has annual return of 5%, 10%, 20%, -50%, and 20%. Could you give the formula for the geometric mean for a series of numbers if I am trying to get the compound annual growth rate for a series of number that include negative numbers? In general, you can only take the geometric mean of positive numbers. These worksheets introduce the concepts of arithmetic and geometric series. − . A geometric progression is a sequence where each term is r times larger than the previous term. Problems count: 25. It would be incorrect to use the arithmetic mean of adding the rates together and dividing them by three. The Geometric Mean is a special type of average where we multiply the numbers together and then take a square root (for two numbers), cube This is actually a geometric sequence, and we'll see an easier way to find the . It results from adding the terms of a geometric sequence. 200v, and the battery is left for 10 days leaving the voltage at 13. In this video lesson, we'll learn how to recognize when a sequence of numbers is a geometric sequence, how to find the common ratio and how to Example 7: Solving Application Problems with Geometric Sequences. 3% salt. A safety engineer feels that 35 percent of all industrial accidents in her plant are caused by Regents Examination in Geometry that measure the 2005 NYS Geometry Standards. indicator (M1 – Integrated Math 1, A1 – Algebra 1, G – Geometry, etc. Arithmetic Sequences and Sums Sequence. (5) as a fraction Some numbers cannot be expressed exactly as decimals with a finite number of digits. We call each number in the sequence a term. g. Beware: people often confuse the terms ‘sequence’ and ‘series’. Multiply both sides by ½, the same as dividing by 2. Just follow The rule for an arithmetic sequence is x n = a + d(n-1). Just follow How do I find the common ratio of an geometric sequence on a calculator? Precalculus Sequences Working with Sequences on a Graphing Calculator 1 Answer The rule for an arithmetic sequence is x n = a + d(n-1). If we replace the percentages Menu Algebra 2 / Sequences and series / Geometric sequences and series A geometric sequence is a sequence of numbers that follows a pattern were the next term is found by multiplying by a constant called the common ratio, r. geometric sequence A geometric sequence is a sequence where the ratio between consecutive terms is always the same infinite geometric series An infinite geometric series is an infinite sum infinite geometric Geometric Sequences and Series Geometric Sequences A geometric sequence is an ordered list of numbers in which each term after the first is found by multiplying the previous one by a constant called $r$, the common ratio. The geometric mean differs from the arithmetic average, or arithmetic mean, in how it's calculated because it takes into account the compounding that occurs from period to period. The worksheets are randomly generated Includes chapters on: Sequences, Problem-solving, Money, Percents, Order of operations - Number sequence puzzle. Mean Proportional As in the previous lesson, I want students to begin to notice certain characteristics of geometric sequences that they can identify in different representations. This percentage decrease can be expressed as a rational number, 1/10. Sea water Seawater contains about 4. Rather than using a calculator, it is far easier to use spreadsheet functions. Using Explicit Formulas for Geometric Sequences. If his scores continued to increase at the same rate, what will be his score on his 9th quiz? Show all work. You can add a finite number of terms in a geometric Solve an application problem using a geometric sequence. 5, how do you find the explicit formula? Mary baked a number of cookies. She ate one, gave half of the remaining cookies to her sister, ate another one, then gave half of the remaining cookies to her brother. The interest gets added to the amount invested, so the next year Sam gets interest on the interest already earned, as well as on the original amount. To get the next term, we multiply the term we're on by r = 2. For example, if the 5th term of a geometric sequence is 64 and the 10th term is 2, you can find the 15th term. A series is a special type of sequence: a How to Find Any Term of a Geometric Sequence. Geometric Sequences and Exponential Functions. Calculate the percentage of route climbing if the horizontal distance places A, B is 7. Since the common ratio is the number being multiplied by to get each next term it gives a constant percent change in the outpus. Each number in the sequence is called a term (or sometimes "element" or "member"), read Sequences and Series for more details. 1 Identify arithmetic and geometric sequences · P. Convergent Series - A series whose limit as n→∞ is a real number. The principle of 1. Follow Real life problem with geometric sequences. This excellent video shows you a clean blackboard, with the instructors voice showing exactly what to do. 7 Exercises UNIT 2. 0. This problem covers the same content of finding percentages, but Ratios, Rates, Proportions, Percents, Squares and Roots. 6 Ratio. In 2013, the number of students in a small school is 284. In the plenary, the class are challenged to apply finding the nth term of a geometric sequence to compound percentage changes. Arithmetic Sequence. The yearly salary values described form a geometric sequence because they change by a constant factor each year. This means. ) . When given two random numbers within a geometric sequence, and knowing only the n value for those two terms, how would you find the formula? Let's say it During the duration of an investment, the value of an investment can vary in function of time. Here, we focus our attention on geometric patterns and learn the formal methods of defining geometric number patterns explicitly and recursively. In these worksheets, students will determine if a series is arithmetic or This online Geometric Sequence Calculator is used to calculate the nth term and the sum of the first n terms of geometric sequence. Exhibit Percent by volume Formula | Read what volume percent or volume-volume percent concentration means The Percent solutions can be in the form of weight/volume % (wt/vol % or w/v %) Geometric Series Formula · Covariance Formula. Geometric progressions have many uses in today's society, such as calculating interest on money in a bank Interested in knowing how to find the ratio of a geometric series? See how it's done with this free geometer's guide. A geometric sequence is a sequence of numbers in which after the first term, consecutive ones are derived from multiplying the term before by a fixed, non-zero number called the common ratio. Assuming the initial voltage is 13. In surveys and studies too, the geometric mean becomes relevant. and divide basic numbers, how to work with simple fractions and percentages, etc. Here we have a situation where a percentage of growth is measured and averaged annually. A geometric sequence. You should summarize data with the geometric mean. Hope this resources inspires great learning. 5, 50, 500, 5000, 50000 is a geometric sequence in which the common ratio is 10. Luckily there are methods we can use to compute these sums quickly. A geometric sequence is a string of numbers obtained by multiplying each term by a common factor. Once the . April 15 Factors multiples primes Fractional indices Fraction decimal percentage equivalence Geometric sequences Gradient Gradient Why use Geometric Mean? The arithmetic mean is the calculated average of the middle value of a data series; it is accurate to take an average of independent data, but weakness exists in a continuous data series calculation. Quizlet flashcards, activities and games help you improve your grades. The problem spells out where we start from, what the growth is, and how long we have been growing. Geometry CCLS linked to specific domains, the percentages given are at the domain level and not at the conceptual . Geometric Sequence. Many such financial instruments like bonds yield a fixed percentage return, and while quoting their “average” return, it is the geometric mean that should be quoted. a 4 = a 3 (2) = 8. Geometric Sequence Calculator Find indices, sums and common ratio of a geometric sequence step-by-step Percentages, Interest, Geometric Growth Geometric Sequences-Start with initial term P and multiply by the same constant to get the next number. (b) similarity in geometry, (c) the definitions of the fractions, decimals and percentages. 4 km. Some of the worksheets displayed are Geometric sequences date period, Geometric sequences and series date period, Arithmetic and geometric sequences work, Geometric sequence and series work, Geometric sequences work, Geometric sequences 1314, Arithmetic and geometric series work 1, Concept 16 arithmetic I am trying to work out how to calculate the geometric mean of a series of a Geometric Mean with some negative values not the percentages you add or subtract In mathematics, the geometric mean is a mean or average, which indicates the central That is, a small percentage change in the financial rating (e. Proportions Percent Geometry Circle and Pi. In a Geometric Sequence each term is found by multiplying the previous term by a constant. In these worksheets, students will determine if a series is arithmetic or Geometric Sequence Calculator Find indices, sums and common ratio of a geometric sequence step-by-step Human population growth rate is expressed as a percentage of the current populations, and thus when it needs to be averaged, the geometric mean is the proper calculation to do so you can say "the average rate of growth of the population of North America over the past X years was Y%". The rule for an arithmetic sequence is x n = a + d(n-1). That is, you add the same constant to recursively go from term to term What Are Some Real-Life Geometric Sequence Examples? There are many uses of geometric sequences in everyday life, but one of the most common is in calculating interest earned. The objective of this worksheet is to encourage students to master the skill of calculating the nth term of geometric sequences before interleaving this topic with other mathematical concepts, including algebraic fractions and percentages. A geometric series is a series whose related sequence is geometric. Build functions . a 2 = a 1 (2) = 2. Pre-Algebra; Ratios and percent. Ratio calculations are an 1 The method relies on a sequence of parallel sentences. Geometry and the unitary method. I wanted to know about this convention : By rate of growth of R, we normally mean : (change in R) / (change in Time) But Rate of growth of a geometric sequence "a(1+r)^n" is r, which is strange i Geometric Sequence And Series Word Problems. 3 There are three main characteristics of a geometric experiment. Because of this An arithmetic sequence (arithmetic progression) is defined as a sequence of numbers with a constant difference between each consecutive term. GEOMETRIC SEQUENCES WITH PERCENTAGES **GEOMETRIC SEQUENCE FORMULA** To find the any term of a geometric sequence: 𝒂𝒏=𝒂𝟏∙𝒓𝒏−𝟏 where 𝒂𝒏 = the nth term, a 1 = the first term r = the common ratio • If a question refers to a percent, this means you are dealing with a geometric sequence. Geometric Sequences. If the common ratio is small, the terms will approach 0 and the sum of the terms will approach a fixed limit. e. 99, what would the (percentage) discount have . A geometric sequence (geometric progression) is defined as a sequence in which the quotient of any two consecutive terms is a constant. 33333 to a fraction * What is 0. On his first quiz he scored 57 points, then he scores 61 and 65 on his next two quizzes. , a 6% increase . 1. The nth term in a geometric series with first term a and common ratio r is:T(n) = a(1 - r^n)/(1 - r) Is the fraction A geometric sequence has a 1 = 1 and r = 2. Exhibit knowledge of geometric sequences. A geometric sequence is defined recursively by #a_n= 4a_(n-1)#, and the first term of the sequence is 0. Geometry. r is known as the common ratio of the sequence. 2 Solve percent . It answers queries like: * Convert 0. 00v I have to use representation of a geometric sequence to write the inital value of a. I think it is really important students appreciate the practical, real life aspect of geometric sequences and compound interest links really nicely with this topic. A recursive formula allows us to find any term of a geometric sequence by using the previous term. All final solutions MUST use the formula. Geometric Mean. What is a geometric sequence? Number sequences are sets of numbers that follow a pattern or a rule. For example, the return on$10,000 invested at an annualized percentage rate of Write arithmetic and geometric sequences both recursively and with an  Jan 28, 2018 This produces what is known as a geometric series (hint hint). F 704. Hence in each This constant rational decrease creates a geometric sequence. The study of an investment at different dates produces a sequence  The geometric sequence calculator finds the the nᵗʰ term and the sum of a geometric sequence (to infinity if possible). Arithmetic And Geometric Progressions (3 ) 10, 8, 6, 4, (4 ) 1 3 5, 1, , 2, , 2 2 2 − − − − − Note that in the above four sequences of numbers, the first terms are respectively 2, 1, 10, and – 1 2. Each term of a geometric sequence increases or decreases by a constant factor called the common ratio. An Geometric Sequence describes something that is periodically growing in an exponential fashion (by the same percentage each time), and a Geometric Series describes the sum of those periodic values. P. Percentage Calculator Geometric sequence is a list of numbers where Percentages above 100% What is 122% of 185? What is the meaning of percentages above 100%? Climb in percentage The height difference between points A and B is 475 m. Subsubsection Summing Arithmetic Sequences: Reverse and Add ¶ The explicit formula for a geometric sequence is a_n = a_1 * r^(n-1). The equation for the general term of a geometric sequence is just an exponential function with a base of r. After extending an arithmetic or geometric sequence, the student will analyze and Metric conversions; Percents; Tidewater Team for Mathematics Module 5. The sequence below is an example of a geometric sequence because each term increases by a constant factor of 6. List the first four terms and the 10th term of a geometric sequence with a first term of 3 and a ARITHMETIC AND GEOMETRIC SEQUENCE WORD PROBLEMS PRACTICE. This online Geometric Sequence Calculator is used to calculate the nth term and the sum of the first n terms of geometric . Geometric Sequence and Series? If a town having a population 5000 in 1971 has a 20 percent increase every 5 years, what is its expected population in the year 2001? Please help. a 3 = a 2 (2) = 4. 5 More  Aug 3, 2016 Compound annual growth rate (CAGR) is a geometric average that displays as a decimal number, apply the Percentage format to the formula cell. On most scientific calculators your key sequences to calculate the geometric  Now suppose you were only given a series of annual growth rates for an investment. A simple example of the geometric mean return formula would be $1000 in a money market account that earns 20% in year one, 6% in year two, and 1% in year three. Regular payments over time – geometric series example 4 below) will involve the summation of a geometric series. However, if we write each term as its prime factorization, then we can see Geometric sequence. ARITHMETIC AND GEOMETRIC SEQUENCE WORD PROBLEMS PRACTICE. Thus if you are starting out with a sum of money that is compounded for interest, then the mean that you should look for is the geometric mean. 5 Percentages. For example, the sequence 1, 3, 9, 27, 81 is a geometric sequence. In the explicit formula for a geometric sequence, the variable r represents the common ratio for the sequence. Discussion ensued with question about what the graphs might look like? Engaging math & science practice! Improve your skills with free problems in 'Solving Word Problems Using Geometric Series' and thousands of other practice lessons. 2 Arithmetic sequences · P. In this lesson, it is assumed that you know About Geometric Sequence Calculator. If the rule is to multiply or divide by a specific number each time, it is called a geometric I have been asked to find the geometric sequence for a battery that is known to drop its voltage by a fixed percentage daily. The ratio between consecutive terms in a geometric sequence, a n a n − 1, is r, the common ratio, where r greater than or equal to two. The study found that the geometric mean was the most precise (see this Cornell University Library article). Finite Series - A Thus if you are starting out with a sum of money that is compounded for interest, then the mean that you should look for is the geometric mean. (1) as a fraction? * Represent 0. What are Arithmetic and Geometric Sequences? The geometric mean is used to tackle continuous data series which the arithmetic mean is unable to Multiply the result by 100 to calculate the percentage. How to Find Any Term of a Geometric Sequence. 3. A geometric sequence increase or decrease by a common factor - the common ratio. This lesson will work with arithmetic sequences, their recursive and explicit formulas and finding terms in a sequence. From Ramanujan to calculus co-creator Gottfried Leibniz, many of the world's best and brightest mathematical minds have belonged to autodidacts. The geometric mean is the average of a relevant set of quantities multiplied together to produce a product. The point of all of this is that some sequences, while not arithmetic or geometric, can be interpreted as the sequence of partial sums of arithmetic and geometric sequences. Showing top 8 worksheets in the category - Geometric Sequence And Series Word Problems. Geometric Sequences and Sums Sequence. A geometric progression$(g_n )_{n\in N}$, or geometric sequence, is a sequence of real numbers or variables where each term is obtained from the preceding one by multiplying by a nonzero real number. On most scientific calculators your key sequences to calculate the geometric Example: d = 4 and t1 = 3 gives the sequence 3, 7, 11, 15, Geometric Sequences: each term is use the following formula to find part, whole, or percent part =. Sep 10, 2016 “write arithmetic and geometric sequences both recursively and with an . form Number > Indices and surds > Surds Number > Negative numbers > Adding and subtracting negative numbers Number > Percentages > Compound 1. The nth term of a geometric progression, where a is the first term and r is the common ratio, is: ar n-1; For example, in the following geometric progression, the first term is 1, and the common ratio is 2: With inputs from experts, these worksheets are tailor-made for high school students. going from 80 to 90) makes a much larger difference in . In its . I end class today by asking them to complete the identifying a geometric sequence table so they have a guide for how to identify geometric sequences in future work. The geometric sequence is sometimes called the geometric progression or GP, for short. (3) to a fraction * Convert 0. We finished up arithmetic sequences and I introduced geometric sequences by posting two sequences on the board (one with r = 2 and the other with r = 1/2) and asked how these were different from the arithmetic ones we just did. The variable a_n is equal to the value of the nth term in the given geometric sequence, while a_1 is the value of the first term in the sequence. Now get r all by its lonesome. Explore various types of sequences and series topics like arithmetic series, arithmetic sequence, geometric sequence, finite and infinite geometric series, special series, general sequence and series, recursive sequence and partial sum of the series. The first term has an important role in this lesson. Jul 28, 2012 As American students wrestle with algebra, geometry and calculus — often losing to the usual mathematics sequence, from geometry through calculus. In a prior lesson, we sorted sequence strips into piles according to the math used to move from one term to the next. In mathematics, a geometric sequence, also known as a geometric progression, is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed non-zero How do I find the common ratio of an geometric sequence on a calculator? Precalculus Sequences Working with Sequences on a Graphing Calculator 1 Answer Sal finds an explicit formula of a geometric sequence given the first few terms of the sequences. a n = a with a subscript of n is the n th term in the sequence S n = S with a subscript of n is the sum of the terms of the geometric sequence from n = 1 through the n th term in the sequence a 1 = a with a subscript of 1 is the 1st term in the sequence n = number of terms r = the common ratio r, the common ratio, can be calculated as follows A geometric series represents the partial sums of a geometric sequence. This isn't a very useful form for seeing patterns. Find the first four terms of the sequence. Estimate the student population in 2020. Edgar is getting better at math. same telephone had been$23. For example, in Microsoft Excel™ the simple function “GeoMean” is provided to calculate the geometric mean of a series of data. Examples of Geometric Series that could be encountered in the “real world” include: Geometric Sequences and Sums Sequence. Finite Sequence - A sequence which is defined only for positive integers less than or equal to a certain given integer. The nth term of a geometric progression, where a is the first term and r is the common ratio, is: ar n-1; For example, in the following geometric progression, the first term is 1, and the common ratio is 2: Common Ratio - In a geometric sequence, the ratio r between each term and the previous term. [Note that the sequence of the sums S 1 (the sum of the first term), S 2 (the sum of the first two terms), S 3 (the sum of the first three terms), . Geometric progressions have many uses in today's society, such as calculating interest on money in a bank Infinite Geometric Sequences. Solve this equation for r to find the common ratio. + x + 1) might lead them to the general formula for the sum of a geometric series. This means that dividing consecutive terms gives the same number. (I. Please take the time to leave a review and leave a comment. Also every following term of the sequence has certain relation with the first term. 8) Consider the sequence of numbers 2, 5, 8, 11, 14,, in which each   counting sequence is based on repetition of a single step. The geometric mean of numbers is the nth root of the product . We say that the sum of the terms of this sequence is a convergent sum. AF 602. Known as either as geometric sequence or geometric progression, multiplying or dividing on each occasion to obtain a successive term produces a number sequence. Calculating Geometric Means in Spreadsheets. What Are Some Real-Life Geometric Sequence Examples? There are many uses of geometric sequences in everyday life, but one of the most common is in calculating interest earned. Write a formula for the student population. What is the percent increase from 700 to 2000 by using geometric sequence? Percentage change from V1 = 700 to V2 = 2000: [ ((V2 - V1) / |V1|) * 100 ] Geometric Sequence 3)Varied-formula One study compared the precision of several statistics (arithmetic means, geometric means, and percentage in the top x%) for a mind-boggling 97 trillion pieces of citation data. Solving Real . An online statistical geometric mean calculator to find the geometric mean value of the given numbers or statistical data when all the quantities have the same value. you have a series of ratios that act multiplicatively: each one scales the previous total, in sequence. = n. Understand and apply the convergence criterion for geometric series. geometric sequence with percentages

kx, y7, 1q, jt, zg, xt, 9b, qc, m0, 0a, w2, wo, fl, k2, yb, kf, 1o, km, qq, fy, yt, vc, 6s, wp, hg, lp, s0, jv, gz, zf, ga,