Chapter 6.4, Problem 61E

To determine

To determine whether the sequence is arithmetic

If the sequence is arithmetic then find common difference.

Answer to Problem 61E

No, the sequence is arithmetic because the difference between each term is not same

Explanation of Solution

Given information:

Given sequence

  $-5,-8,-12,-17,\mathrm{......}$

Concept used:

A sequence is said to be arithmetic if the difference in all pairs of consecutive or successive terms of the sequence always remain same or constant.

This constant difference in all pairs of consecutive or successive terms of the sequence is called common difference $\left(d\right)$

Given sequence

  $-5,-8,-12,-17,\mathrm{......}$

Find difference in each consecutive pair of sequence

  $\begin{array}{l}{d}_1=-8-\left(-5\right)=-8+5=-3\\ d_2=-12-\left(-8\right)=-12+8=-4\\ d_3=-17-\left(-12\right)=-17+12=-5\end{array}$

(where $d_1,d_2,d_3$ represents difference between consecutive pairs)

Clearly,

  $d_1\ne d_2\ne d_3$

Therefore,

Given sequence $-5,-8,-12,-17,\mathrm{......}$ is not arithmetic.