Use the Formula for the Sum of the First n Terms of a Geometric Sequence
-Find the sum of the first 10 terms of the geometric sequence: $\frac { 1 } { 6 } , - \frac { 1 } { 3 } , \frac { 2 } { 3 } , - \frac { 4 } { 3 } , \frac { 8 } { 3 } , \ldots$
A) $- \frac { 341 } { 6 }$
B) $- \frac { 343 } { 6 }$
C) $- \frac { 167 } { 3 }$
D) $- \frac { 347 } { 6 }$

Question

Quizplus · Accepted Answer

The first term is $\frac { 1 } { 6 }$ and the common ratio is -3. So, the sum of the first 10 terms is:$$S_{10} = \frac { \frac { 1 } { 6 } (1 - (-3)^{10}) } { 1 - (-3) } = \frac { \frac { 1 } { 6 } (1 - 59049) } { 4 } = - \frac { 341 } { 6 }$$

Use the Formula for the Sum of the First N 16,−13,23,−43,83,…\frac { 1 } { 6 } , - \frac { 1 } { 3 } , \frac { 2 } { 3 } , - \frac { 4 } { 3 } , \frac { 8 } { 3 } , \ldots61​,−31​,32​,−34​,38​,…

Use the Formula for the Sum of the First N $\frac { 1 } { 6 } , - \frac { 1 } { 3 } , \frac { 2 } { 3 } , - \frac { 4 } { 3 } , \frac { 8 } { 3 } , \ldots$