수열 전체 문제

Write a recursive formula for the geometric sequence $1,\,-\frac{1}{2},\,\frac{1}{4},\,-\frac{1}{8},\ldots$

Write an explicit formula for the geometric sequence $4,\,-\frac{4}{3},\,\frac{4}{9},\,-\frac{4}{27},\ldots$

Use summation notation to write the sum of terms $3{k}^{2}-\frac{5}{6}k$ from $k=-3$ to $k=15.$

A community baseball stadium has 10 seats in the first row, 13 seats in the second row, 16 seats in the third row, and so on. There are 56 rows in all. What is the seating capacity of the stadium?

Use the formula for the sum of the first $n$ terms of a geometric series to find $\sum_{k=1}^{7}-0.2\cdot {(-5)}^{k-1}.$

Find the sum of the infinite geometric series $\sum_{k=1}^{\infty }\frac{1}{3}\cdot {\left(-\frac{1}{5}\right)}^{k-1}.$

Ramla deposits $3,600 into a retirement fund each year. The fund earns 7.5% annual interest, compounded monthly. If she opened her account when she was 20 years old, how much will she have by the time she’s 55? How much of that amount was interest earned?

In a competition of 50 professional ballroom dancers, 22 compete in the fox-trot competition, 18 compete in the tango competition, and 6 compete in both the fox-trot and tango competitions. How many dancers compete in the fox-trot or tango competitions?

A buyer of a new sedan can custom order the car by choosing from 5 different exterior colors, 3 different interior colors, 2 sound systems, 3 motor designs, and either manual or automatic transmission. How many choices does the buyer have?

To allocate annual bonuses, a manager must choose his top four employees and rank them first to fourth. In how many ways can he create the “Top-Four” list out of the 32 employees?

A music group needs to choose 3 songs to play at the annual Battle of the Bands. How many ways can they choose their set if they have 15 songs to pick from?

A self-serve frozen yogurt shop has 8 candy toppings and 4 fruit toppings to choose from. How many ways are there to top a frozen yogurt?

Use the Binomial Theorem to expand ${\left(\frac{3}{2}x-\frac{1}{2}y\right)}^{5}.$

Find the seventh term of ${\left({x}^{2}-\frac{1}{2}\right)}^{13}$ without fully expanding the binomial.

For the following exercises, use the spinner in (the referenced figure).

Construct a probability model showing each possible outcome and its associated probability. (Use the first letter for colors.)

For the following exercises, use the spinner in (the referenced figure).

What is the probability of landing on an odd number?

For the following exercises, use the spinner in (the referenced figure).

What is the probability of landing on blue?

For the following exercises, use the spinner in (the referenced figure).

What is the probability of landing on blue or an odd number?

For the following exercises, use the spinner in (the referenced figure).

What is the probability of landing on anything other than blue or an odd number?

For the following exercises, use the spinner in (the referenced figure).

A bowl of candy holds 16 peppermint, 14 butterscotch, and 10 strawberry flavored candies. Suppose a person grabs a handful of 7 candies. What is the percent chance that exactly 3 are butterscotch? (Show calculations and round to the nearest tenth of a percent.)