<< Chapter < Page Chapter >> Page >

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

3 ,   12 ,   48 ,   192 ,   768

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

a n = 1 5 ( 1 3 ) n 1

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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 ) .

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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?

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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
Got questions? Get instant answers now!

Find the sum of the infinite geometric series k = 1 45 ( 1 3 ) k 1 .

S = 135 4

Got questions? Get instant answers now!

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.)

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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?

Got questions? Get instant answers now!

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

Got questions? Get instant answers now!

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?

Got questions? Get instant answers now!

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

10 4 = 10 , 000

Got questions? Get instant answers now!

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?

Got questions? Get instant answers now!

Calculate P ( 18 , 4 ) .

P ( 18 , 4 ) = 73 , 440

Got questions? Get instant answers now!

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?

Got questions? Get instant answers now!

Calculate C ( 15 , 6 ) .

C ( 15 , 6 ) = 5005

Got questions? Get instant answers now!

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?

Got questions? Get instant answers now!
Practice Key Terms 9

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Algebra and trigonometry' conversation and receive update notifications?

Ask