For the given geometric sequence, find the limit of the infinite series, if it exists.
-$$- 15 , - 5 , - \frac { 5 } { 3 } , - \frac { 5 } { 9 } , \ldots$$
A) $- 15$

B) $- \frac { 45 } { 2 }$

C) $\frac { 15 } { 2 }$

D) $- \frac { 65 } { 3 }$

Question

For the given geometric sequence, find the limit of the infinite series, if it exists.
-$$- 15 , - 5 , - \frac { 5 } { 3 } , - \frac { 5 } { 9 } , \ldots$$
A) $- 15$

B) $- \frac { 45 } { 2 }$

C) $\frac { 15 } { 2 }$

D) $- \frac { 65 } { 3 }$

Quizplus · Accepted Answer

The given sequence is a geometric series with the first term $a = -15$ 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 $a = -15$ and $r = \frac{1}{3}$, we get $S = \frac{-15}{1 - \frac{1}{3}} = \frac{-15}{\frac{2}{3}} = -\frac{45}{2}$.

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