Chapter 12.2, Problem 16E

To determine

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

Answer to Problem 16E

Yes, the term is in arithmetic sequence and the common difference is $2$ .

Explanation of Solution

Given:

It is given in the question that the term are $2,4,6,8,\mathrm{..............}$ .

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 $2,4,6,8,\mathrm{..............}$ .

Subtract every two consecutive terms,

  $\begin{array}{l}4-2=2\\ 6-4=2\\ 8-6=2\end{array}$

After subtracting ,it is seen that all have same constant so, these terms can be the terms of an arithmetic sequence.

Now, to find the common difference d ,subtract two consecutive terms

  $4-2=2$ .

Conclusion:

Yes, the term is in arithmetic sequence and the common difference is $2$ .