Chapter 11.1, Problem 21PPS

To determine

To find out whether sequence is arithmetic or not.

Answer to Problem 21PPS

No , the sequence is not arithmetic

Explanation of Solution

Given:

  

Formula used;

  

Calculation:

  $\begin{array}{l}{a}_1=\frac{1}{2}\\ a_2=\frac{1}{3}\\ a_3=\frac{1}{4}\\ a_4=\frac{1}{5}\\ \\ d=a_2-a_1\\ =\frac{1}{3}-\frac{1}{2}\\ =\frac{-1}{6}\\ d=a_3-a_2\\ =\frac{1}{4}-\frac{1}{3}\\ =\frac{-1}{12}\\ \text{The common difference is not same}\text{.}\\ \therefore \text{ the sequence is not arithemetic}\text{.}\end{array}$