Find the sum of the terms in the geometric sequence.
-$4 , - 1 , \frac { 1 } { 4 } , - \frac { 1 } { 16 } , \ldots$
A)3
B)4
C) $\frac { 16 } { 5 }$
D)- 1

Question

Quizplus · Accepted Answer

The given sequence is a geometric sequence with the first term $a = 4$ and common ratio $r = -\frac{1}{4}$. The sum of an infinite geometric series can be found using the formula $S = \frac{a}{1 - r}$, where $S$ is the sum, $a$ is the first term, and $r$ is the common ratio. Substituting the given values, we get $S = \frac{4}{1 - (-\frac{1}{4})} = \frac{4}{\frac{5}{4}} = \frac{16}{5}$.

Find the Sum of the Terms in the Geometric Sequence 4,−1,14,−116,…4 , - 1 , \frac { 1 } { 4 } , - \frac { 1 } { 16 } , \ldots4,−1,41​,−161​,…

Find the Sum of the Terms in the Geometric Sequence $4 , - 1 , \frac { 1 } { 4 } , - \frac { 1 } { 16 } , \ldots$