Chapter 6.5, Problem 14E

To determine

To find:Whether the sequence $-25,-18,-11,-\mathrm{4...}$ is arithmetic, geometric or neither.

Answer to Problem 14E

The sequence $-25,-18,-11,-\mathrm{4...}$ isarithmetic.

Explanation of Solution

Given information:The sequence $-25,-18,-11,-\mathrm{4...}$

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.

A sequence is said to be geometric sequence if every term of the sequence, after the first term, is obtained by multiplying a constant to the preceding term. The constant is known as common ratio.

Here, the 1^st term $=-25$

Difference between 1^st and 2^nd term $=-18-(-25)=-18+25=7$

Difference between 2^nd and 3^rd term $=-11-(-18)=-11+18=7$

Difference between 3^rd and 4^th term $=-4-(-11)=-4+11=7$

And so on.

Since, each term of the sequence is obtained by adding a constant 7 to the preceding term, the sequence is not arithmetic.