Chapter 8.2, Problem 8E

To determine

To verify: whether the sequence is arithmetic.

Answer to Problem 8E

The sequence is not arithmetic.

Explanation of Solution

Given information:

  $81,27,9,3,1,\mathrm{........}$ .

Formula used:

Arithmetic difference − the difference of consecutive term is constant. The constant difference is called the common difference and is denoted by d .

Therefore,

  $d=a_{n+1}-a_n;n\ge 1$ .

Calculation:

Consider ,

  $81,27,9,3,1,\mathrm{........}$

Now,

  $\begin{array}{l}=a_2-a_1=27-81=-54\\ =a_3-a_2=9-27=-18\\ =a_4-a_3=3-9=-6\\ =a_5-a_4=1-3=-2\end{array}$

Each difference is different .

So, the sequence is not arithmetic.