Chapter 8, Problem 53RE

a)

To determine

Check whether $b_1,b_2,\dots b_n$ is an arithmetic sequence or not for the given condition $b_n=\left|a_n\right|$.

b)

To determine

Check whether $b_1,b_2,\dots b_n$ is an arithmetic sequence or not for the given condition $b_n=a_n+8$.

c)

To determine

Check whether $b_1,b_2,\dots b_n$ is an arithmetic sequence or not for the given condition $b_n=7a_n$.

d)

To determine

Check whether $b_1,b_2,\dots b_n$ is an arithmetic sequence or not for the given condition $b_n=\frac{1}{a_n}$.

e)

To determine

Check whether $b_1,b_2,\dots b_n$ is an arithmetic sequence or not for the given condition $b_n=\log a_n$.

f)

To determine

Check whether $b_1,b_2,\dots b_n$ is an arithmetic sequence or not for the given condition $b_n=a_n^3$.