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: 5, 10, 20, 40, 80, . . . .
A) 10,235
B) 10,215
C) 10,272
D) 10,237

Question

Quizplus · Accepted Answer

The sum of the first n terms of a geometric sequence is given by the formula $ S_n = a \frac{r^n - 1}{r - 1} $, where $ a $ is the first term, $ r $ is the common ratio, and $ n $ is the number of terms. Here, $ a = 5 $, $ r = 2 $, and $ n = 11 $. Plugging these values into the formula gives $ S_{11} = 5 \frac{2^{11} - 1}{2 - 1} = 5 \times (2048 - 1) = 5 \times 2047 = 10,235 $.

Use the Formula for the Sum of the First N