Chapter 6.5, Problem 61E

To determine

To find:Whether the sequence $9,18,36,\mathrm{72...}$ is arithmetic. If so, what the common difference is.

Answer to Problem 61E

No the sequence $9,18,36,\mathrm{72...}$ is not arithmetic.

Explanation of Solution

Given information:The sequence $9,18,36,\mathrm{72...}$

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 $=9$

Difference between 1^st and 2^nd term $=18-9=9$

Difference between 2^nd and 3^rd term $=36-18=18$

Difference between 3^rd and 4^th term $=72-36=36$

And so on.

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