Find the sum of the geometric series.
-$$4 - 8 + 16 - 32 + 64 - \ldots + 4 \cdot ( - 2 ) ^ { 11 }$$
A) $- 5453$
B) $- 5462$
C) $- 5460$
D) $- 5466$

Question

Quizplus · Accepted Answer

The given series is a geometric series with the first term $a = 4$ and common ratio $r = -2$. The sum of the first $n$ terms of a geometric series is given by $S_n = \frac{a(1 - r^n)}{1 - r}$, where $n$ is the number of terms. Here, $n = 12$ because the series goes up to $( - 2 )^{11}$, which is the 12th term. Plugging in the values, we get $S_{12} = \frac{4(1 - (-2)^{12})}{1 - (-2)} = \frac{4(1 - 4096)}{3} = \frac{4(-4095)}{3} = -4 \cdot 1365 = -5460$.

Find the Sum of the Geometric Series 4−8+16−32+64−…+4⋅(−2)114 - 8 + 16 - 32 + 64 - \ldots + 4 \cdot ( - 2 ) ^ { 11 }4−8+16−32+64−…+4⋅(−2)11

Find the Sum of the Geometric Series $4 - 8 + 16 - 32 + 64 - \ldots + 4 \cdot ( - 2 ) ^ { 11 }$