Answer:
The common ratio is [tex]\frac{1}{x^4}[/tex]
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 [tex]n^{th}[/tex] term of a geometric sequence is represented by [tex]a_n=ar^{n-1}[/tex].
The [tex]1^{st}[/tex] term of the sequence = a.
The sum of first n term is
[tex]S_n=\frac{a(1-r^n)}{1-r}[/tex]
The common ratio = r.
Given geometric sequence,
[tex]\frac{1}{x^{10}}[/tex] , [tex]\frac{1}{x^{14}}[/tex], [tex]\frac{1}{x^{18}}[/tex],[tex]\frac{1}{x^{22}}[/tex] ........
The common ratio is
[tex]=\frac{\textrm{second term}}{\textrm{first term}}[/tex]
[tex]=\frac{\frac{1}{x^{14}}}{\frac{1}{x^{10}}}[/tex]
[tex]=\frac{x^{10}}{x^{14}}[/tex]
[tex]=\frac{1}{x^4}[/tex]
