13.7 Probability  (Page 8/18)

What are the first five terms of the geometric sequence $a_1=3,a_n=4\cdot a_{n-1}?$

Write a recursive formula for the geometric sequence $1,\frac{1}{3},\frac{1}{9},\frac{1}{27},\dots$

Write an explicit formula for the geometric sequence $-\frac{1}{5},-\frac{1}{15},-\frac{1}{45},-\frac{1}{135},\dots$

How many terms are in the finite geometric sequence $-5, -\frac{5}{3}, -\frac{5}{9},\dots , -\frac{5}{59\text{,}049}?$

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

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, … .

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 $12,6,3,\frac{3}{2},\dots$

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?

Find the sum of the infinite geometric series ${\displaystyle \sum }_{k=1}^{\infty }45\cdot {(-\frac{1}{3})}^{k-1}.$

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?

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?

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

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?

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

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

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?