Chapter 9.2, Problem 7PPSE

Solution

To find: If the sequence $10,20,30,40,\dots$ is arithmetic or not. If yes, find the common difference.

Sequence is arithmetic and common difference is $10$ .

Given information:

The sequence, $10,20,30,40,\dots$ .

Formula used:

Difference between two consecutive terms of an arithmetic sequence is common and the difference is called common difference.

The nth term of an arithmetic sequence is given by $a_n=a+\left(n-1\right)d$ , where $a$ is the first term and $d$ is the common difference.

Calculation:

Observe the difference between the consecutive terms.

  $\begin{array}{c}20-10=10\\ 30-20=10\\ 40-30=10\end{array}$

Since difference between the consecutive terms are common, the sequence is arithmetic, and the common difference is $10$ .

Conclusion:

Sequence is arithmetic and common difference is $10$ .