Chapter 11.2, Problem 89STP

To determine

Determine whether the sequence $10,8,5,\mathrm{1.......}$ is arithmetic or not.

Answer to Problem 89STP

No, the sequence is not Arithmetic.

Explanation of Solution

Given:

The sequence:$10,8,5,\mathrm{1.......}$

Concept Used:

A sequence is a set of numbers, called terms, arranged in some particular order.

An arithmetic sequence is a sequence with the difference between two consecutive terms constant. The difference is called the common difference.

A geometric sequence is a sequence with the ratio between two consecutive terms constant.

Calculation:

First Term: $a_1=10$

Common Difference for Arithmetic sequence:

  $d=\text{2nd}\text{term}-\text{1st}\text{term =}8-10=-2\text{or}d=\text{3rd}\text{term}-\text{2nd}\text{term}\text{=}5-8=-3$

The common difference is not constant, so the sequence is not arithmetic.

Thus, no, the sequence is not rithmetic.