Use the Formula for the Sum of the First n Terms of a Geometric Sequence
-Find the sum of the first 11 terms of the geometric sequence: 4, -12, 36, -108, 324, . . . .
A)177,148
B)177,146
C)177,155
D)177,142

Question

Quizplus · Accepted Answer

The sum of the first n terms of a geometric sequence can be found using the formula $S_n = \frac{a(1 - r^n)}{1 - r}$, where $a$ is the first term, $r$ is the common ratio, and $n$ is the number of terms. For this sequence, $a = 4$, $r = -3$ (since each term is -3 times the previous one), and $n = 11$. Plugging these values into the formula gives $S_{11} = \frac{4(1 - (-3)^{11})}{1 - (-3)} = \frac{4(1 + 177147)}{4} = 177148$.

Use the Formula for the Sum of the First N