234k views
5 votes
Find the sum of an infinite geometric series where a1 = 180, and the common ratio is r = 3∕4 ?A) 240B) 720C) 135D) 360

User Sunhwan Jo
by
6.6k points

1 Answer

1 vote

Answer:

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

User Michael Rodriguez
by
6.8k points