91Ó°ÊÓ

Casey said that the formula for the sum of a geometric series could be written as \(S_{n}=\frac{a_{1}-a_{n} r}{1-r} .\) Do you agree with Casey? Justify your answer.

Nichelle said that sequence of numbers in which each term equals half of the previous term is a finite sequence. Randi said that is an infinite sequence. Who is correct? Justify your answer.

In \(3-14 :\) a. Write each arithmetic series as the sum of terms. b. Find each sum. $$ \sum_{n=1}^{10} 3 n $$

In \(3-14,\) determine whether each given sequence is geometric. If it is geometric, find \(r\) . If it is not geometric, explain why it is not. $$ 1,-3,9,-27,81, \dots $$

An infinitely repeating decimal is an infinite geometric series. Find the rational number represented by each of the following infinitely repeating decimals. \(1.11111 \ldots=1+0.1+0.01+0.001+\cdots\)

In \(3-18,\) write the first five terms of each sequence. $$ a_{n}=2 n-1 $$

An infinitely repeating decimal is an infinite geometric series. Find the rational number represented by each of the following infinitely repeating decimals. 0.444444\(\ldots\)

In \(15-22 :\) a. Write each sum as a series. b. Find the sum of each series. $$ 3+\sum_{n=1}^{5} 3(2)^{n} $$

Write the first six terms of the arithmetic sequence that has 12 for the first term and 42 for the sixth term.

In \(15-26,\) write each series in sigma notation. $$ 3+5+7+9+11+13+15 $$