Find the sum of the geometric series. 7 + (-14) + 28 + (-56) + 112
A) 21
B) -147
C) -35
D) 77

Question

Quizplus · Accepted Answer

The series is a geometric series with the first term $a = 7$ and the 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, $n = 5$, so $S_5 = \frac{7(1 - (-2)^5)}{1 - (-2)} = \frac{7(1 + 32)}{3} = \frac{7 \times 33}{3} = 7 \times 11 = 77$.

Find the Sum of the Geometric Series