Chapter 8.5, Problem 107E

To determine

To check: if the given sequence is arithmetic, geometric or neither and explain.

Answer to Problem 107E

Arithmetic sequence.

Explanation of Solution

Given information: We have given a sequence $26,18,10,2,-6,\mathrm{.....}$

First of all we need to check the differences of next terms to previous terms of the given sequence.

  $\begin{array}{l}{d}_1=a_2-a_1=18-26=-8\\ d_2=a_3-a_2=10-18=-8\\ d_3=a_4-a_3=2-10=-8\\ d_4=a_5-a_4=-6-2=-8\end{array}$

We could see that differences of next terms to previous terms are same. Therefore, it’s an Arithmetic sequence.