Find the indicated sum. Use the formula for the sum of the first n terms of a geometric sequence.
-$$\sum _ { i = 1 } ^ { 8 } \left( \frac { 4 } { 3 } \right) ^ { i }$$
A) $\frac { 235,900 } { 6561 }$
B) $\frac { 58,975 } { 2187 }$
C) $- \frac { 14,197 } { 2187 }$
D) $- \frac { 56,788 } { 6561 }$

Question

Quizplus · Accepted Answer

The sum of the first n terms of a geometric sequence is given by $S_n = \frac{a(1 - r^n)}{1 - r}$, where $a$ is the first term, $r$ is the common ratio, and $n$ is the number of terms. Here, $a = \left(\frac{4}{3}\right)^1 = \frac{4}{3}$, $r = \frac{4}{3}$, and $n = 8$. Plugging these values into the formula gives $S_8 = \frac{\frac{4}{3}(1 - (\frac{4}{3})^8)}{1 - \frac{4}{3}} = \frac{\frac{4}{3}(1 - \frac{65536}{6561})}{-\frac{1}{3}} = \frac{235,900}{6561}$.

Find the Indicated Sum ∑i=18(43)i\sum _ { i = 1 } ^ { 8 } \left( \frac { 4 } { 3 } \right) ^ { i }i=1∑8​(34​)i

Find the Indicated Sum $\sum _ { i = 1 } ^ { 8 } \left( \frac { 4 } { 3 } \right) ^ { i }$