Use a graphing utility to find the sum of the geometric sequence. Round answer to two decimal places, if necessary.
-$- 5 - 15 - 45 - 135 - 405 - \cdots - 5 \cdot 3 ^ { 9 }$
A) $- 147,620$
B) $- 147,618$
C) $- 147,583$
D) $- 147,640$

Question

Quizplus · Accepted Answer

The sum of a geometric sequence can be found using 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. Here, $a_1 = -5$, $r = 3$, and $n = 10$ (since the sequence goes up to $3^9$, and including the first term makes 10 terms). Plugging these values into the formula gives $S_{10} = \frac{-5(1 - 3^{10})}{1 - 3}$, which simplifies to $-147,620$ when rounded to two decimal places.

Use a Graphing Utility to Find the Sum of the Geometric