Find the sum of the infinite geometric series.
-$- 12 - 3 - \frac { 3 } { 4 } - \frac { 3 } { 16 } - \ldots$ . . .
A)- 16
B) $- \frac { 63 } { 4 }$
C)-12
D)4

Question

Quizplus · Accepted Answer

The given series is a geometric series with the first term $a = -12$ and common ratio $r = \frac{1}{4}$. The sum of an infinite geometric series is given by $S = \frac{a}{1 - r}$, where $|r| < 1$. Substituting the given values, we get $S = \frac{-12}{1 - \frac{1}{4}} = \frac{-12}{\frac{3}{4}} = -16$.

Find the Sum of the Infinite Geometric Series −12−3−34−316−…- 12 - 3 - \frac { 3 } { 4 } - \frac { 3 } { 16 } - \ldots−12−3−43​−163​−…

Find the Sum of the Infinite Geometric Series $- 12 - 3 - \frac { 3 } { 4 } - \frac { 3 } { 16 } - \ldots$