Question

Find the common ratio of the geometric sequence.

Answer 1

Answer:

The common ratio is $\frac{1}{x^4}$

Step-by-step explanation:

Geometric sequence:A geometric sequence is a sequence in which the ratio of any term to the preceding term of that term is always constant.

Common ratio: The ratio of any term to the  preceding term of that term.

The $n^{th}$ term of a geometric sequence is represented by  $a_n=ar^{n-1}$.

The $1^{st}$ term of the sequence = a.

The sum of first n term is

$S_n=\frac{a(1-r^n)}{1-r}$

The common ratio = r.

Given geometric sequence,

$\frac{1}{x^{10}}$ , $\frac{1}{x^{14}}$, $\frac{1}{x^{18}}$,$\frac{1}{x^{22}}$ ........

The common ratio is

$=\frac{\textrm{second term}}{\textrm{first term}}$

$=\frac{\frac{1}{x^{14}}}{\frac{1}{x^{10}}}$

$=\frac{x^{10}}{x^{14}}$

$=\frac{1}{x^4}$