Chapter 8.RE, Problem 51RE

To determine

(a)

To find:

Whether the sequence $b_1,b_2, {\dots ,b}_n$ an arithmetic sequence if $b_n=\left|a_n\right|$ given that $a_1,a_2, {\dots ,a}_n$ is an arithmetic sequence.

To determine

(b)

To find:

Whether the sequence $b_1,b_2, {\dots ,b}_n$ an arithmetic sequence if $b_n=a_n+8$ given that $a_1,a_2, {\dots ,a}_n$ is an arithmetic sequence.

To determine

(c)

To find:

Whether the sequence $b_1,b_2, {\dots ,b}_n$ an arithmetic sequence if $b_n={7a}_n$ given that $a_1,a_2, {\dots ,a}_n$ is an arithmetic sequence.

To determine

(d)

To find:

Whether the sequence $b_1,b_2, {\dots ,b}_n$ an arithmetic sequence if $b_n=\frac{1}{a_n}$ given that $a_1,a_2, {\dots ,a}_n$ is an arithmetic sequence.

To determine

(e)

To find:

Whether the sequence $b_1,b_2, {\dots ,b}_n$ an arithmetic sequence if $b_n={\log a}_n$ given that $a_1,a_2, {\dots ,a}_n$ is an arithmetic sequence.

To determine

(f)

To find:

Whether the sequence $b_1,b_2, {\dots ,b}_n$ an arithmetic sequence if $b_n=a_n^3$ given that $a_1,a_2, {\dots ,a}_n$ is an arithmetic sequence.