Find the partial sum of the geometric sequence with the given first term and common ratio.
-$9 , a _ { 1 } = \frac { 1 } { 4 } , r = - 3$
A) $\frac { 4915 } { 4 }$

B) $\frac { 4921 } { 4 }$

C) 1232

D) $\frac { 4919 } { 4 }$

Question

Find the partial sum of the geometric sequence with the given first term and common ratio.
-$9 , a _ { 1 } = \frac { 1 } { 4 } , r = - 3$
A) $\frac { 4915 } { 4 }$

B) $\frac { 4921 } { 4 }$

C) 1232

D) $\frac { 4919 } { 4 }$

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. Given $a_1 = \frac{1}{4}$ and $r = -3$, and since we're looking for the sum of the first 9 terms, we substitute $n = 9$, $a_1 = \frac{1}{4}$, and $r = -3$ into the formula to get $S_9 = \frac{\frac{1}{4}(1 - (-3)^9)}{1 - (-3)}$. Simplifying this gives $S_9 = \frac{\frac{1}{4}(1 - (-19683))}{4}$, which simplifies further to $S_9 = \frac{4921}{4}$.

Find the Partial Sum of the Geometric Sequence with the Given