Find the sum of the terms in the geometric sequence.
-$4 , \frac { 4 } { 5 } , \frac { 4 } { 25 } , \frac { 4 } { 125 } , \ldots$ . .
A)5
B) $\frac { 24 } { 5 }$
C)4
D) $\frac { 4 } { 5 }$

Question

Quizplus · Accepted Answer

The given sequence is a geometric sequence with the first term $a = 4$ and common ratio $r = \frac{1}{5}$. The sum of an infinite geometric series is given by $S = \frac{a}{1 - r}$, provided $|r| < 1$. Substituting the given values, we get $S = \frac{4}{1 - \frac{1}{5}} = \frac{4}{\frac{4}{5}} = 5$.

Find the Sum of the Terms in the Geometric Sequence 4,45,425,4125,…4 , \frac { 4 } { 5 } , \frac { 4 } { 25 } , \frac { 4 } { 125 } , \ldots4,54​,254​,1254​,…

Find the Sum of the Terms in the Geometric Sequence $4 , \frac { 4 } { 5 } , \frac { 4 } { 25 } , \frac { 4 } { 125 } , \ldots$