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What are the first five terms of the geometric sequence a 1 = 3 ,   a n = 4 a n 1 ?

3 ,   12 ,   48 ,   192 ,   768

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Write a recursive formula for the geometric sequence 1 ,   1 3 ,   1 9 ,   1 27 ,

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Write an explicit formula for the geometric sequence 1 5 ,   1 15 ,   1 45 ,   1 135 ,

a n = 1 5 ( 1 3 ) n 1

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How many terms are in the finite geometric sequence 5 ,   5 3 ,   5 9 , ,   5 59 , 049 ?

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Series and Their Notation

Use summation notation to write the sum of terms 1 2 m + 5 from m = 0 to m = 5.

m = 0 5 ( 1 2 m + 5 ) .

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Use summation notation to write the sum that results from adding the number 13 twenty times.

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Use the formula for the sum of the first n terms of an arithmetic series to find the sum of the first eleven terms of the arithmetic series 2.5, 4, 5.5, … .

S 11 = 110

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A ladder has 15 tapered rungs, the lengths of which increase by a common difference. The first rung is 5 inches long, and the last rung is 20 inches long. What is the sum of the lengths of the rungs?

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Use the formula for the sum of the first n terms of a geometric series to find S 9 for the series 12 ,   6 ,   3 ,   3 2 ,

S 9 23.95

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The fees for the first three years of a hunting club membership are given in [link] . If fees continue to rise at the same rate, how much will the total cost be for the first ten years of membership?

Year Membership Fees
1 $1500
2 $1950
3 $2535
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Find the sum of the infinite geometric series k = 1 45 ( 1 3 ) k 1 .

S = 135 4

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A ball has a bounce-back ratio of 3 5 the height of the previous bounce. Write a series representing the total distance traveled by the ball, assuming it was initially dropped from a height of 5 feet. What is the total distance? ( Hint : the total distance the ball travels on each bounce is the sum of the heights of the rise and the fall.)

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Alejandro deposits $80 of his monthly earnings into an annuity that earns 6.25% annual interest, compounded monthly. How much money will he have saved after 5 years?

$5,617.61

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The twins Sarah and Scott both opened retirement accounts on their 21 st birthday. Sarah deposits $4,800.00 each year, earning 5.5% annual interest, compounded monthly. Scott deposits $3,600.00 each year, earning 8.5% annual interest, compounded monthly. Which twin will earn the most interest by the time they are 55 years old? How much more?

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Counting Principles

How many ways are there to choose a number from the set { 10 , 6 , 4 , 10 , 12 , 18 , 24 , 32 } that is divisible by either 4 or 6 ?

6

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In a group of 20 musicians, 12 play piano, 7 play trumpet, and 2 play both piano and trumpet. How many musicians play either piano or trumpet?

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How many ways are there to construct a 4-digit code if numbers can be repeated?

10 4 = 10 , 000

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A palette of water color paints has 3 shades of green, 3 shades of blue, 2 shades of red, 2 shades of yellow, and 1 shade of black. How many ways are there to choose one shade of each color?

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Calculate P ( 18 , 4 ) .

P ( 18 , 4 ) = 73 , 440

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In a group of 5 freshman, 10 sophomores, 3 juniors, and 2 seniors, how many ways can a president, vice president, and treasurer be elected?

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Calculate C ( 15 , 6 ) .

C ( 15 , 6 ) = 5005

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A coffee shop has 7 Guatemalan roasts, 4 Cuban roasts, and 10 Costa Rican roasts. How many ways can the shop choose 2 Guatemalan, 2 Cuban, and 3 Costa Rican roasts for a coffee tasting event?

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Practice Key Terms 9

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Source:  OpenStax, College algebra. OpenStax CNX. Feb 06, 2015 Download for free at https://legacy.cnx.org/content/col11759/1.3
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