For the given geometric sequence, find the limit of the infinite series, if it exists.
-$$45,15,5 , \frac { 5 } { 3 } , \ldots$$
A) 45
B) $\frac { 135 } { 2 }$
C) 65
D) $- \frac { 45 } { 2 }$

Question

Quizplus · Accepted Answer

The given sequence is a geometric series with the first term $a = 45$ 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 $a = 45$ and $r = \frac{1}{3}$, we get $S = \frac{45}{1 - \frac{1}{3}} = \frac{45}{\frac{2}{3}} = \frac{45 \times 3}{2} = \frac{135}{2}$.

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