Determine whether the infinite geometric series converges or diverges. If it converges, find its sum.
-12 + 6 + 3 + ...
A)Converges; 24
B)Converges; - 12
C)Converges; 21
D)Diverges

Question

Quizplus · Accepted Answer

The series is a geometric series with the first term $a = 12$ and common ratio $r = \frac{1}{2}$. A geometric series converges if $|r| < 1$, which is true in this case. The sum of a converging geometric series is given by $S = \frac{a}{1 - r}$, so substituting $a = 12$ and $r = \frac{1}{2}$ gives $S = \frac{12}{1 - \frac{1}{2}} = \frac{12}{\frac{1}{2}} = 24$.

Determine Whether the Infinite Geometric Series Converges or Diverges