Use the Formula for the Sum of the First n Terms of a Geometric Sequence
-Find the sum of the first 14 terms of the geometric sequence: $\frac { 1 } { 4 } , - \frac { 3 } { 4 } , \frac { 9 } { 4 } , - \frac { 27 } { 4 } , \frac { 81 } { 4 } , \ldots$
A) $- \frac { 597871 } { 2 }$
B) $- 298936$
C)$ - \frac { 1195735 } { 4 }$
D) $- 298937$

Question

Quizplus · Accepted Answer

The first term is $\frac { 1 } { 4 } $ and the common ratio is -3. So, the sum of the first 14 terms is:$$S_{14} = \frac { \frac { 1 } { 4 } (1 - (-3)^{14}) } { 1 - (-3) } = \frac { \frac { 1 } { 4 } (1 - 4782969) } { 4 } = - \frac { 597871 } { 2 }$$

Use the Formula for the Sum of the First N 14,−34,94,−274,814,…\frac { 1 } { 4 } , - \frac { 3 } { 4 } , \frac { 9 } { 4 } , - \frac { 27 } { 4 } , \frac { 81 } { 4 } , \ldots41​,−43​,49​,−427​,481​,…

Use the Formula for the Sum of the First N $\frac { 1 } { 4 } , - \frac { 3 } { 4 } , \frac { 9 } { 4 } , - \frac { 27 } { 4 } , \frac { 81 } { 4 } , \ldots$