For the given geometric sequence, find the limit of the infinite series, if it exists.
-$3,1, \frac{1}{3}, \frac{1}{9}, \ldots$
A) $\frac{9}{2}$
B) 4
C) 3
D) 1

Question

Quizplus · Accepted Answer

The given sequence is a geometric series with the first term $a = 3$ 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 $a = 3$ and $r = \frac{1}{3}$, we get $S = \frac{3}{1 - \frac{1}{3}} = \frac{3}{\frac{2}{3}} = \frac{9}{2}$.

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