Find the partial sum of the geometric sequence with the given first term and common ratio.
-$\mathrm { s } 5 , \mathrm { a } 1 = 1 , \mathrm { r } = \frac { 1 } { 2 }$
A) $- \frac { 1 } { 48 }$
B) $\frac { 1 } { 12 }$
C) 93
D) $\frac { 31 } { 16 }$

Question

Quizplus · Accepted Answer

The formula for the sum of the first $n$ terms of a geometric sequence is $S_n = \frac{a_1(1 - r^n)}{1 - r}$, where $a_1$ is the first term, $r$ is the common ratio, and $n$ is the number of terms. Plugging in $a_1 = 1$, $r = \frac{1}{2}$, and $n = 5$, we get $S_5 = \frac{1(1 - (\frac{1}{2})^5)}{1 - \frac{1}{2}} = \frac{1 - \frac{1}{32}}{\frac{1}{2}} = \frac{31}{32} \times 2 = \frac{31}{16}$.

Find the Partial Sum of the Geometric Sequence with the Given