For the given geometric sequence, find the limit of the infinite series, if it exists.
-$$4 , - \frac { 4 } { 3 } , \frac { 4 } { 9 } , - \frac { 4 } { 27 } , \ldots$$
A) 3
B) $- \frac { 4 } { 3 }$
C) 4
D) $\frac { 8 } { 3 }$

Question

Quizplus · Accepted Answer

The given sequence is a geometric series with the first term $a = 4$ and common ratio $r = -\frac{1}{3}$. The sum of an infinite geometric series is given by $S = \frac{a}{1 - r}$ if $|r| < 1$. Substituting $a = 4$ and $r = -\frac{1}{3}$, we get $S = \frac{4}{1 - (-\frac{1}{3})} = \frac{4}{\frac{4}{3}} = 3$.

For the Given Geometric Sequence, Find the Limit of the Infinite