Solve the problem.
-If $\mathrm { a } _ { 1 }$ is 1 , and $\mathrm { r }$ is $\frac { 1 } { 4 }$, find $\mathrm { S } _ { 5 }$.
A) $\frac { 341 } { 256 }$
B) $\frac { 5 } { 384 }$
C) 341
D) $\frac { 1 } { 192 }$

Question

Quizplus · Accepted Answer

The sum of the first 5 terms of a geometric series is given by $S_n = \frac{a_1(1 - r^n)}{1 - r}$, where $a_1$ is the first term, $r$ is the common ratio, and $n$ is the number of terms. Plugging in $a_1 = 1$, $r = \frac{1}{4}$, and $n = 5$, we get $S_5 = \frac{1(1 - (\frac{1}{4})^5)}{1 - \frac{1}{4}} = \frac{1 - \frac{1}{1024}}{1 - \frac{1}{4}} = \frac{1 - \frac{1}{1024}}{\frac{3}{4}} = \frac{1024 - 1}{768} = \frac{1023}{768} = \frac{341}{256}$.

Solve the Problem a1\mathrm { a } _ { 1 }a1​

Solve the Problem $\mathrm { a } _ { 1 }$