The explicit formula is [tex]a_{n}[/tex] = a[tex]r^{n-1}[/tex]
For the Geometric sequence, the explicit formula for the nth term is
[tex]a_{n}[/tex] = a[tex]r^{n-1}[/tex]
Where,
a = first number of the series
r = common ratio
n = number of series
[tex]a_{1}[/tex] = a
[tex]a_{2}[/tex] = ar
[tex]a_{3}[/tex] = a [tex]r^{2}[/tex]
.....
Therefore the series is a, ar, a[tex]r^{2}[/tex], a[tex]r^{3}[/tex],,,,.....
Here we have the series 25, 5, 1, 1/5
Here common ratio = 1/5
and if we want to find the 5th term the formula is
[tex]a_{5}[/tex] = 25 ×[tex](\frac{1}{5} )^{4}[/tex]
= [tex]\frac{1}{25}[/tex]
To know more about the explicit formula of the geometric sequence refer to the link given below:
https://brainly.com/question/24198356
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