Chapter 6.5, Problem 62E

To determine

To find:Whether the sequence $-5,-8,-12,-\mathrm{17....}$ is arithmetic. If so, what the common difference is.

Answer to Problem 62E

No the sequence $-5,-8,-12,-\mathrm{17....}$ is not arithmetic.

Explanation of Solution

Given information:The sequence $-5,-8,-12,-\mathrm{17....}$

Calculation:A sequence is said to be arithmetic sequence if every term of the sequence, after the first term, is obtained by adding a constant to the preceding term. The constant is known as common difference.

Here, the 1^st term $=-5$

Difference between 1^st and 2^nd term $=-8-(-5)=-8+5=-3$

Difference between 2^nd and 3^rd term $=-12-(-8)=-12+8=-4$

Difference between 3^rd and 4^th term $=-17-(-12)=-17+12=-5$

And so on.

Since, the difference between the terms does not remain constant the sequence is not arithmetic.