Find the indicated sum. Use the formula for the sum of the first n terms of a geometric sequence.
-$$\sum _ { i = 1 } ^ { 5 } \frac { 2 } { 3 } \cdot 2 ^ { i }$$
A) $\frac { 124 } { 3 }$
B) $\frac { 100 } { 3 }$
C) $\frac { 148 } { 3 }$
D) $\frac { 136 } { 3 }$

Question

Quizplus · Accepted Answer

The sum of the first n terms of a geometric sequence is given by the formula $$S_n = \frac{a(1 - r^n)}{1 - r}$$, where $a$ is the first term, $r$ is the common ratio, and $n$ is the number of terms. In this case, the first term $a = \frac{2}{3} \cdot 2^1 = \frac{4}{3}$, the common ratio $r = 2$, and $n = 5$. Plugging these values into the formula gives $$S_5 = \frac{\frac{4}{3}(1 - 2^5)}{1 - 2} = \frac{\frac{4}{3}(1 - 32)}{-1} = \frac{\frac{4}{3} \cdot -31}{-1} = \frac{124}{3}$$.

Find the Indicated Sum ∑i=1523⋅2i\sum _ { i = 1 } ^ { 5 } \frac { 2 } { 3 } \cdot 2 ^ { i }i=1∑5​32​⋅2i

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