Question

Find the sum of an infinite geometric series where a1 = 180, and the common ratio is r = 3∕4 ?A) 240B) 720C) 135D) 360

Answer 1

The sum to infinity of the geometric series is;

`S_(\infty)=720`

Step-by-step explanation:

Given an infinite geometric series where;

`\begin{gathered} a_1=180 \\ r=(3)/(4) \end{gathered}`

Recall that the sum to infinity of a geometric series can be calculated using the formula;

`S_(\infty)=(a_1)/(1-r)`

substituting the given values;

`\begin{gathered} S_(\infty)=(a_1)/(1-r)=(180)/(1-(3)/(4))=(180)/((1)/(4))=180*4 \\ S_(\infty)=720 \end{gathered}`

Therefore, the sum to infinity of the geometric series is;

`S_(\infty)=720`