Find the sum of the finite geometric sequence.
$$\sum _ { n = 1 } ^ { 5 } - \left( - \frac { 1 } { 6 } \right) ^ { n - 1 }$$
A) $\frac { 6665 } { 1296 }$
B) $- \frac { 1 } { 6 }$
C) 1111
D) $\frac { 185 } { 216 }$
E) $- \frac { 1111 } { 1296 }$

Question

Quizplus · Accepted Answer

The sum of a geometric sequence is given by $ S_n = a \frac{1-r^n}{1-r} $, where $ a $ is the first term and $ r $ is the common ratio. Here, $ a = -1 $ and $ r = -\frac{1}{6} $. Calculating $ S_5 $ gives $- \frac { 1111 } { 1296 }$.

Find the Sum of the Finite Geometric Sequence ∑n=15−(−16)n−1\sum _ { n = 1 } ^ { 5 } - \left( - \frac { 1 } { 6 } \right) ^ { n - 1 }n=1∑5​−(−61​)n−1

Find the Sum of the Finite Geometric Sequence $\sum _ { n = 1 } ^ { 5 } - \left( - \frac { 1 } { 6 } \right) ^ { n - 1 }$