Answer:
Option 1
Step-by-step explanation:
Given expression representing the partial sum of the geometric series,
[tex]\sum_{n=1}^{n=4}(125)(\frac{1}{5})^{n-1}[/tex]
Expression that represents the sum of a geometric series is,
[tex]\sum_{n=1}^{n}(a)(r)^{n-1}[/tex]
Here, n = number of terms
a = first term
r = common ratio
By comparing both the expressions,
n = 4
a = 125
r = [tex]\frac{1}{5}[/tex]
From the given options,
Option 1
First term 'a' = 125
Common ratio 'r' = [tex]\frac{25}{125}[/tex] = [tex]\frac{1}{5}[/tex]
Number of terms 'n' = 4
Therefore, Option 1 will be the correct option.
