# 13.7 Probability  (Page 8/18)

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What are the first five terms of the geometric sequence

Write a recursive formula for the geometric sequence

Write an explicit formula for the geometric sequence

${a}_{n}=-\frac{1}{5}\cdot {\left(\frac{1}{3}\right)}^{n-1}$

How many terms are in the finite geometric sequence

## Series and Their Notation

Use summation notation to write the sum of terms $\frac{1}{2}m+5$ from $m=0$ to $m=5.$

$\sum _{m=0}^{5}\left(\frac{1}{2}m+5\right).$

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

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, … .

${S}_{11}=110$

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?

Use the formula for the sum of the first n terms of a geometric series to find ${S}_{9}$ for the series

${S}_{9}\approx 23.95$

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 Find the sum of the infinite geometric series $\sum _{k=1}^{\infty }45\cdot {\left(-\frac{1}{3}\right)}^{k-1}.$ $S=\frac{135}{4}$ A ball has a bounce-back ratio of $\frac{3}{5}$ 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.) 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 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?

## Counting Principles

How many ways are there to choose a number from the set $\text{\hspace{0.17em}}\left\{-10\text{,}-6\text{,}4\text{,}10\text{,}12\text{,}18\text{,}24\text{,}32\right\}\text{\hspace{0.17em}}$ that is divisible by either $4$ or $6?$

6

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?

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

${10}^{4}=10\text{,}000$

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?

Calculate $P\left(18,4\right).$

$P\left(18,4\right)=73\text{,}440$

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?

Calculate $C\left(15,6\right).$

$C\left(15,6\right)=5005$

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?

#### Questions & Answers

The sequence is {1,-1,1-1.....} has
circular region of radious
how can we solve this problem
Sin(A+B) = sinBcosA+cosBsinA
Prove it
Eseka
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?
find the sum of 28th term of the AP 3+10+17+---------
I think you should say "28 terms" instead of "28th term"
Vedant
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
write down the polynomial function with root 1/3,2,-3 with solution
if A and B are subspaces of V prove that (A+B)/B=A/(A-B)
write down the value of each of the following in surd form a)cos(-65°) b)sin(-180°)c)tan(225°)d)tan(135°)
Prove that (sinA/1-cosA - 1-cosA/sinA) (cosA/1-sinA - 1-sinA/cosA) = 4
what is the answer to dividing negative index
In a triangle ABC prove that. (b+c)cosA+(c+a)cosB+(a+b)cisC=a+b+c.
give me the waec 2019 questions
the polar co-ordinate of the point (-1, -1)