수열 전체 문제

An arithmetic sequence has the first term ${a}_{1}=18$ and common difference $d=-8.$ What are the first five terms?

An arithmetic sequence has terms ${a}_{3}=11.7$ and ${a}_{8}=-14.6.$ What is the first term?

Write a recursive formula for the arithmetic sequence $-20,-10,0,10,\ldots$

Write a recursive formula for the arithmetic sequence $0,\,-\frac{1}{2},\,-1,\,-\frac{3}{2},\ldots ,$ and then find the 31^st term.

Write an explicit formula for the arithmetic sequence $\frac{7}{8},\,\frac{29}{24},\,\frac{37}{24},\,\frac{15}{8},\ldots$

How many terms are in the finite arithmetic sequence $12,20,28,\ldots ,172?$

Find the common ratio for the geometric sequence $2.5,\,5,\,10,\,20,\ldots$

Is the sequence 4, 16, 28, 40 … geometric? If so find the common ratio. If not, explain why.

A geometric sequence has terms ${a}_{7}=16,384$ and ${a}_{9}=262,144$. What are the first five terms?

A geometric sequence has the first term ${a}_{1}=-3$ and common ratio $r=\frac{1}{2}.$ What is the 8^th term?

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 $1,\,\frac{1}{3},\,\frac{1}{9},\,\frac{1}{27},\ldots$

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, … .

Use the formula for the sum of the first n terms of a geometric series to find ${S}_{9}$ for the series $12,\,6,\,3,\,\frac{3}{2},\ldots$

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

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?