Find the indicated sum.
-$a _ { 1 } = 3 , r = \frac { 1 } { 2 } ; \text { find } s _5$
A) $\frac { 93 } { 16 }$
B) $\frac { 3 } { 8 }$
C) $\frac { 3 } { 16 }$
D)93

Question

Quizplus · Accepted Answer

The sum of the first 5 terms 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, $a_1 = 3$, $r = \frac{1}{2}$, and $n = 5$, we get $s_5 = 3 \frac{1 - (\frac{1}{2})^5}{1 - \frac{1}{2}} = 3 \frac{1 - \frac{1}{32}}{\frac{1}{2}} = 3 \frac{\frac{31}{32}}{\frac{1}{2}} = 3 \cdot \frac{31}{16} = \frac{93}{16}$.

Find the Indicated Sum a1=3,r=12; find s5a _ { 1 } = 3 , r = \frac { 1 } { 2 } ; \text { find } s _5a1​=3,r=21​; find s5​

Find the Indicated Sum $a _ { 1 } = 3 , r = \frac { 1 } { 2 } ; \text { find } s _5$