Chapter 11.1, Problem 34PPS

To determine

The sequence $124,\text{ 18}6,248,\mathrm{.....}$ is geometric. Yes or no.

Answer to Problem 34PPS

No, it is not a geometric sequence.

Explanation of Solution

Given:

The sequence: $124,\text{ 18}6,248,\mathrm{.....}$

Concept Used:

In mathematics, a geometric progression, also known as a geometric sequence, is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.

For example, the sequence $2,6,18,54,\mathrm{...}$ is a geometric progression with common ratio 3.

The ratio of 2^nd term and first term is called the common ratio.

  $\text{Common}\text{ratio}=r=\frac{\text{2nd}\text{term}}{\text{1st}\text{term}}=\frac{\text{3rd}\text{term}}{\text{2nd}\text{term}}$

Calculation:

The sequence: $124,\text{ 18}6,248,\mathrm{.....}$

First term: $a_1=124$ ; $\text{Common}\text{ratio}=r=\frac{\text{2nd}\text{term}}{\text{1st}\text{term}}=\frac{186}{124}=\frac{3}{2}$ or $r=\frac{\text{3rd}\text{term}}{\text{2nd}\text{term}}=\frac{248}{186}=\frac{4}{3}$

The common ratios are not equal $\frac{3}{2}\ne \frac{4}{3}$ . So, it is not a geometric sequence.

Thus, no, it is not a geometric sequence.