For the given geometric sequence, find the limit of the infinite series, if it exists.
-$-10,-5,-\frac{5}{2},-\frac{5}{4}, \ldots$
A) -20
B) $-\frac{35}{2}$
C) 10
D) - 10

Question

Quizplus · Accepted Answer

The given sequence is a geometric series with the first term $a = -10$ and common ratio $r = \frac{1}{2}$. The sum of an infinite geometric series is given by $S = \frac{a}{1 - r}$ if $|r| < 1$. Substituting the given values, $S = \frac{-10}{1 - \frac{1}{2}} = \frac{-10}{\frac{1}{2}} = -20$.

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