Question

Which equation represents the partial sum of the geometric series?

Answer 1

Answer:

Option 1

Step-by-step explanation:

Given expression representing the partial sum of the geometric series,

$\sum_{n=1}^{n=4}(125)(\frac{1}{5})^{n-1}$

Expression that represents the sum of a geometric series is,

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

Here, n = number of terms

a = first term

r = common ratio

By comparing both the expressions,

n = 4

a = 125

r = $\frac{1}{5}$

From the given options,

Option 1

First term 'a' = 125

Common ratio 'r' = $\frac{25}{125}$ = $\frac{1}{5}$

Number of terms 'n' = 4

Therefore, Option 1 will be the correct option.