Question

Which equation represents the partial sum of the geometric series?

4
Σ (125)(1/5)^n-1
n=1

Answer 1

Option 1

Explanation:

Given expression representing the partial sum of the geometric series,

`\sum_(n=1)^(n=4)(125)((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 =
`(1)/(5)`

From the given options,

Option 1

First term 'a' = 125

Common ratio 'r' =
`(25)/(125)` =
`(1)/(5)`

Number of terms 'n' = 4

Therefore, Option 1 will be the correct option.