Use the formula for $$\mathrm { S } _ { \mathbf { n } }$$ to find the sum of the first five terms of the geometric sequence.
-1, 3, 9, 27, . . .
A) 122
B) 121
C) 131
D) 124

Question

Quizplus · Accepted Answer

The formula for the sum of the first $n$ terms of a geometric sequence is $\mathrm{S}_n = \frac{a(1 - r^n)}{1 - r}$, where $a$ is the first term and $r$ is the common ratio. Here, $a = 1$, $r = 3$, and $n = 5$. Plugging these values into the formula gives $\mathrm{S}_5 = \frac{1(1 - 3^5)}{1 - 3} = \frac{1 - 243}{-2} = 121$.

Use the Formula For Sn\mathrm { S } _ { \mathbf { n } }Sn​

Use the Formula For $\mathrm { S } _ { \mathbf { n } }$