Find the sum of the first n terms of the sequence.
-$- 1 , - 3 , - 9 , \ldots ; \mathrm { n } = 12$
A) $- 265,720$
B) 797,161
C) $- 797,161$
D) $\frac { 797,161 } { 2 }$

Question

Quizplus · Accepted Answer

The common ratio is -3, and the first term is -1. The sum of the first n terms of a geometric sequence is given by the formula:$$S_n = \frac{a_1(1 - r^n)}{1 - r}$$where $a_1$ is the first term, $r$ is the common ratio, and $n$ is the number of terms.In this case, $a_1 = -1$, $r = -3$, and $n = 12$. Substituting these values into the formula, we get:$$S_{12} = \frac{-1(1 - (-3)^{12})}{1 - (-3)} = \frac{-1(1 - 531441)}{4} = -265,720$$Therefore, the sum of the first 12 terms of the sequence is -265,720.

Find the Sum of the First N Terms of the Sequence