Chapter 12.2, Problem 20E

To determine

Find whether the sequence is arithmetic or not. If yes, find the common difference.

Answer to Problem 20E

No, the term is in arithmetic sequence.

Explanation of Solution

Given:

It is given in the question that the term are $\frac{1}{2},\frac{1}{3},\frac{1}{4},\frac{1}{5},\mathrm{..............}$ .

Concept Used:

In this, use the concept of subtracting every two consecutive term , if it is same then it is in arithmetic sequence and the subtraction also gives the common difference.

Calculation: Here, the term is $\frac{1}{2},\frac{1}{3},\frac{1}{4},\frac{1}{5},\mathrm{..............}$ .

Subtract every two consecutive terms,

  $\begin{array}{l}\frac{1}{3}-\frac{1}{2}=\frac{2-3}{6}=-\frac{1}{6}\\ \frac{1}{4}-\frac{1}{3}=\frac{3-4}{12}=-\frac{1}{12}\\ \frac{1}{5}-\frac{1}{4}=\frac{4-5}{20}=-\frac{1}{20}\end{array}$

After subtracting ,it is seen that it did not have the same constant so, these terms can not be the terms of an arithmetic sequence.

Conclusion:

No, the term is in arithmetic sequence.