Chapter 4.7, Problem 3LC

To determine

The common difference and find whether the given sequence is in AP or not.

Answer to Problem 3LC

Sequence is not in AP.

Explanation of Solution

Given :

Arithmetic sequence is given,

  $1,-7,-14,-\mathrm{21.......}$

A sequence is said to be in AP if common difference is same for all term.

Common difference is given by,

  $\text{c}\text{.d = next term - preious term}$

Therefore,

  $\begin{array}{l}{d}_1=-7-1=-8\\ d_2=-14-\left(-7\right)=-14+7=-7\\ d_3=-21-\left(-14\right)=-21+14=-7\end{array}$

Since, all the differences are not same therefore sequence will be not in AP and common difference is -7.