수열 전체 문제

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

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

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

The fees for the first three years of a hunting club membership are given in (the referenced table). 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 $\sum_{k=1}^{\infty }45\cdot {\left(-\frac{1}{3}\right)}^{k-1}.$

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 Hoa and Binh both opened retirement accounts on their 21^st birthday. Hoa deposits $4,800.00 each year, earning 5.5% annual interest, compounded monthly. Binh 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?

Write the first four terms of the sequence defined by the recursive formula $a=-14, {a}_{n}=\frac{2+{a}_{n-1}}{2}.$

Write the first four terms of the sequence defined by the explicit formula ${a}_{n}=\frac{{n}^{2}-n-1}{n!}.$

Is the sequence $0.3,\,1.2,\,2.1,\,3,\ldots$ arithmetic? If so find the common difference.

An arithmetic sequence has the first term ${a}_{1}=-4$ and common difference $d=-\frac{4}{3}.$ What is the 6^th term?

Write a recursive formula for the arithmetic sequence $-2,\,-\frac{7}{2},\,-5,\,-\frac{13}{2},\ldots$ and then find the 22^nd term.

Write an explicit formula for the arithmetic sequence $15.6,\,15,\,14.4,\,13.8,\ldots$ and then find the 32^nd term.

Is the sequence $-2,-1,-\frac{1}{2},-\frac{1}{4},\ldots$ geometric? If so find the common ratio. If not, explain why.

What is the 11^th term of the geometric sequence $-1.5,-3,-6,-12,\ldots ?$