Find the sum of the geometric series.
-$$\sum _ { \mathrm { k } = 1 } ^ { 5 } 4 ( - 2 ) ^ { \mathrm { k } }$$
A) 8
B) 40
C) -340
D) -88

Question

Quizplus · Accepted Answer

The given series is a geometric series with the first term $a = 4(-2)^1 = -8$ and common ratio $r = -2$. The sum of the first $n$ terms of a geometric series is given by $S_n = a\frac{1 - r^n}{1 - r}$, where $n$ is the number of terms. Here, $n = 5$, so the sum is $S_5 = -8\frac{1 - (-2)^5}{1 - (-2)} = -8\frac{1 + 32}{3} = -8 \times 11 = -88$.

Find the Sum of the Geometric Series ∑k=154(−2)k\sum _ { \mathrm { k } = 1 } ^ { 5 } 4 ( - 2 ) ^ { \mathrm { k } }k=1∑5​4(−2)k

Find the Sum of the Geometric Series $\sum _ { \mathrm { k } = 1 } ^ { 5 } 4 ( - 2 ) ^ { \mathrm { k } }$