Find the indicated sum. Use the formula for the sum of the first n terms of a geometric sequence.
-$$\sum _ { \mathrm { i } = 1 } ^ { 5 } \frac { 4 } { 3 } \cdot 2 ^ { \mathrm { i } }$$
A) $\frac { 248 } { 3 }$
B) $\frac { 266 } { 3 }$
C) $\frac { 272 } { 3 }$
D) $\frac { 287 } { 3 }$

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, $a = \frac{4}{3} \cdot 2^1 = \frac{8}{3}$, $r = 2$, and $n = 5$. Plugging these values into the formula gives $S_5 = \frac{\frac{8}{3}(1 - 2^5)}{1 - 2} = \frac{\frac{8}{3}(1 - 32)}{-1} = \frac{8}{3} \cdot 31 = \frac{248}{3}$.

Find the Indicated Sum ∑i=1543⋅2i\sum _ { \mathrm { i } = 1 } ^ { 5 } \frac { 4 } { 3 } \cdot 2 ^ { \mathrm { i } }i=1∑5​34​⋅2i

Find the Indicated Sum $\sum _ { \mathrm { i } = 1 } ^ { 5 } \frac { 4 } { 3 } \cdot 2 ^ { \mathrm { i } }$