Chapter 11.2, Problem 88STP

To determine

Determine whether the sequence $2,\frac{7}{5},\frac{4}{5},\frac{1}{5}\mathrm{.......}$ is arithmetic or not.

Answer to Problem 88STP

Yes, the sequence is Arithmetic.

Explanation of Solution

Given:

The sequence:$2,\frac{7}{5},\frac{4}{5},\frac{1}{5}\mathrm{.......}$

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: $a_1=2$

Common Difference for Arithmetic sequence:

  $\begin{array}{l}d=\text{2nd}\text{term}-\text{1st}\text{term =}\frac{7}{5}-2=\frac{7}{5}-\frac{10}{5}=-\frac{3}{5}\\ \text{or}\\ d=\text{3rd}\text{term}-\text{2nd}\text{term}\text{=}\frac{4}{5}-\frac{7}{5}=-\frac{3}{5}\end{array}$

The common difference is constant, so the sequence is arithmetic.

Thus, yes, the sequence is Arithmetic.