<< 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!

Questions & Answers

show that the set of all natural number form semi group under the composition of addition
Nikhil Reply
explain and give four Example hyperbolic function
Lukman Reply
_3_2_1
felecia
⅗ ⅔½
felecia
_½+⅔-¾
felecia
The denominator of a certain fraction is 9 more than the numerator. If 6 is added to both terms of the fraction, the value of the fraction becomes 2/3. Find the original fraction. 2. The sum of the least and greatest of 3 consecutive integers is 60. What are the valu
SABAL Reply
1. x + 6 2 -------------- = _ x + 9 + 6 3 x + 6 3 ----------- x -- (cross multiply) x + 15 2 3(x + 6) = 2(x + 15) 3x + 18 = 2x + 30 (-2x from both) x + 18 = 30 (-18 from both) x = 12 Test: 12 + 6 18 2 -------------- = --- = --- 12 + 9 + 6 27 3
Pawel
2. (x) + (x + 2) = 60 2x + 2 = 60 2x = 58 x = 29 29, 30, & 31
Pawel
ok
Ifeanyi
on number 2 question How did you got 2x +2
Ifeanyi
combine like terms. x + x + 2 is same as 2x + 2
Pawel
x*x=2
felecia
2+2x=
felecia
Mark and Don are planning to sell each of their marble collections at a garage sale. If Don has 1 more than 3 times the number of marbles Mark has, how many does each boy have to sell if the total number of marbles is 113?
mariel Reply
Mark = x,. Don = 3x + 1 x + 3x + 1 = 113 4x = 112, x = 28 Mark = 28, Don = 85, 28 + 85 = 113
Pawel
how do I set up the problem?
Harshika Reply
what is a solution set?
Harshika
find the subring of gaussian integers?
Rofiqul
hello, I am happy to help!
Shirley Reply
please can go further on polynomials quadratic
Abdullahi
hi mam
Mark
I need quadratic equation link to Alpa Beta
Abdullahi Reply
find the value of 2x=32
Felix Reply
divide by 2 on each side of the equal sign to solve for x
corri
X=16
Michael
Want to review on complex number 1.What are complex number 2.How to solve complex number problems.
Beyan
yes i wantt to review
Mark
use the y -intercept and slope to sketch the graph of the equation y=6x
Only Reply
how do we prove the quadratic formular
Seidu Reply
please help me prove quadratic formula
Darius
hello, if you have a question about Algebra 2. I may be able to help. I am an Algebra 2 Teacher
Shirley Reply
thank you help me with how to prove the quadratic equation
Seidu
may God blessed u for that. Please I want u to help me in sets.
Opoku
what is math number
Tric Reply
4
Trista
x-2y+3z=-3 2x-y+z=7 -x+3y-z=6
Sidiki Reply
can you teacch how to solve that🙏
Mark
Solve for the first variable in one of the equations, then substitute the result into the other equation. Point For: (6111,4111,−411)(6111,4111,-411) Equation Form: x=6111,y=4111,z=−411x=6111,y=4111,z=-411
Brenna
(61/11,41/11,−4/11)
Brenna
x=61/11 y=41/11 z=−4/11 x=61/11 y=41/11 z=-4/11
Brenna
Need help solving this problem (2/7)^-2
Simone Reply
x+2y-z=7
Sidiki
what is the coefficient of -4×
Mehri Reply
-1
Shedrak
Practice Key Terms 9

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play




Source:  OpenStax, College algebra. OpenStax CNX. Feb 06, 2015 Download for free at https://legacy.cnx.org/content/col11759/1.3
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'College algebra' conversation and receive update notifications?

Ask