# 11.7 Probability  (Page 8/18)

 Page 8 / 18

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

a colony of bacteria is growing exponentially doubling in size every 100 minutes. how much minutes will it take for the colony of bacteria to triple in size
I got 300 minutes. is it right?
Patience
no. should be about 150 minutes.
Jason
It should be 158.5 minutes.
Mr
ok, thanks
Patience
what is the importance knowing the graph of circular functions?
can get some help basic precalculus
What do you need help with?
Andrew
how to convert general to standard form with not perfect trinomial
can get some help inverse function
ismail
Rectangle coordinate
how to find for x
it depends on the equation
Robert
whats a domain
The domain of a function is the set of all input on which the function is defined. For example all real numbers are the Domain of any Polynomial function.
Spiro
foci (–7,–17) and (–7,17), the absolute value of the differenceof the distances of any point from the foci is 24.
difference between calculus and pre calculus?
give me an example of a problem so that I can practice answering
x³+y³+z³=42
Robert
dont forget the cube in each variable ;)
Robert
of she solves that, well ... then she has a lot of computational force under her command ....
Walter
what is a function?
I want to learn about the law of exponent
explain this
what is functions?
A mathematical relation such that every input has only one out.
Spiro
yes..it is a relationo of orders pairs of sets one or more input that leads to a exactly one output.
Mubita
Is a rule that assigns to each element X in a set A exactly one element, called F(x), in a set B.
RichieRich
If the plane intersects the cone (either above or below) horizontally, what figure will be created?