Find the indicated sum.
-$a _ { 1 } = \frac { 1 } { 8 } , r = - 2 ; \text { find } s _ { 13 }$
A) $\frac { 2725 } { 8 }$
B) $\frac { 2729 } { 8 }$
C) $\frac { 1369 } { 4 }$
D) $\frac { 2731 } { 8 }$

Question

Quizplus · Accepted Answer

The sum of a geometric series is given by $s_n = a_1 \frac{1 - r^n}{1 - r}$, where $a_1$ is the first term, $r$ is the common ratio, and $n$ is the number of terms. Plugging in the given values, $a_1 = \frac{1}{8}$, $r = -2$, and $n = 13$, we get $s_{13} = \frac{1}{8} \frac{1 - (-2)^{13}}{1 - (-2)} = \frac{1}{8} \frac{1 - (-8192)}{3} = \frac{1 + 8192}{8 \cdot 3} = \frac{8193}{24}$. Simplifying this gives $\frac{2731}{8}$, which matches option D.

Find the Indicated Sum a1=18,r=−2; find s13a _ { 1 } = \frac { 1 } { 8 } , r = - 2 ; \text { find } s _ { 13 }a1​=81​,r=−2; find s13​

Find the Indicated Sum $a _ { 1 } = \frac { 1 } { 8 } , r = - 2 ; \text { find } s _ { 13 }$