# 9.7 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 what is math number Tric Reply x-2y+3z=-3 2x-y+z=7 -x+3y-z=6 Sidiki Reply 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 the operation * is x * y =x + y/ 1+(x × y) show if the operation is commutative if x × y is not equal to -1 Alfred Reply An investment account was opened with an initial deposit of$9,600 and earns 7.4% interest, compounded continuously. How much will the account be worth after 15 years?
lim x to infinity e^1-e^-1/log(1+x)
given eccentricity and a point find the equiation
12, 17, 22.... 25th term
12, 17, 22.... 25th term
Akash
College algebra is really hard?
Absolutely, for me. My problems with math started in First grade...involving a nun Sister Anastasia, bad vision, talking & getting expelled from Catholic school. When it comes to math I just can't focus and all I can hear is our family silverware banging and clanging on the pink Formica table.
Carole
I'm 13 and I understand it great
AJ
I am 1 year old but I can do it! 1+1=2 proof very hard for me though.
Atone
hi
Not really they are just easy concepts which can be understood if you have great basics. I am 14 I understood them easily.
Vedant
find the 15th term of the geometric sequince whose first is 18 and last term of 387
I know this work
salma
The given of f(x=x-2. then what is the value of this f(3) 5f(x+1)
hmm well what is the answer
Abhi
If f(x) = x-2 then, f(3) when 5f(x+1) 5((3-2)+1) 5(1+1) 5(2) 10
Augustine
how do they get the third part x = (32)5/4
make 5/4 into a mixed number, make that a decimal, and then multiply 32 by the decimal 5/4 turns out to be
AJ
how
Sheref
can someone help me with some logarithmic and exponential equations.
sure. what is your question?
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
I don't understand what the A with approx sign and the boxed x mean
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
oops. ignore that.
so you not have an equal sign anywhere in the original equation?
hmm
Abhi
is it a question of log
Abhi
🤔.
Abhi
I rally confuse this number And equations too I need exactly help
salma
But this is not salma it's Faiza live in lousvile Ky I garbage this so I am going collage with JCTC that the of the collage thank you my friends
salma
Commplementary angles
hello
Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
hii
Uday
hi
salma
hi
Ayuba
Hello
opoku
hi
Ali
greetings from Iran
Ali
salut. from Algeria
Bach
hi
Nharnhar