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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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Questions & Answers

A laser rangefinder is locked on a comet approaching Earth. The distance g(x), in kilometers, of the comet after x days, for x in the interval 0 to 30 days, is given by g(x)=250,000csc(π30x). Graph g(x) on the interval [0, 35]. Evaluate g(5)  and interpret the information. What is the minimum distance between the comet and Earth? When does this occur? To which constant in the equation does this correspond? Find and discuss the meaning of any vertical asymptotes.
Kaitlyn Reply
The sequence is {1,-1,1-1.....} has
amit Reply
circular region of radious
Kainat Reply
how can we solve this problem
Joel Reply
Sin(A+B) = sinBcosA+cosBsinA
Eseka Reply
Prove it
Eseka
Please prove it
Eseka
hi
Joel
June needs 45 gallons of punch. 2 different coolers. Bigger cooler is 5 times as large as smaller cooler. How many gallons in each cooler?
Arleathia Reply
7.5 and 37.5
Nando
find the sum of 28th term of the AP 3+10+17+---------
Prince Reply
I think you should say "28 terms" instead of "28th term"
Vedant
the 28th term is 175
Nando
192
Kenneth
if sequence sn is a such that sn>0 for all n and lim sn=0than prove that lim (s1 s2............ sn) ke hole power n =n
SANDESH Reply
write down the polynomial function with root 1/3,2,-3 with solution
Gift Reply
if A and B are subspaces of V prove that (A+B)/B=A/(A-B)
Pream Reply
write down the value of each of the following in surd form a)cos(-65°) b)sin(-180°)c)tan(225°)d)tan(135°)
Oroke Reply
Prove that (sinA/1-cosA - 1-cosA/sinA) (cosA/1-sinA - 1-sinA/cosA) = 4
kiruba Reply
what is the answer to dividing negative index
Morosi Reply
In a triangle ABC prove that. (b+c)cosA+(c+a)cosB+(a+b)cisC=a+b+c.
Shivam Reply
give me the waec 2019 questions
Aaron Reply
Practice Key Terms 9

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Source:  OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
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