Find the sum of the indicated terms of the geometric sequence.? $$\sum _ { n = 1 } ^ { n = 8 } 3 ( 4 ) ^ { n - 1 }$$ ?
A)s = 65,535
B)s = 65,538
C)s = 65,532
D)s = 65,541
E)s = 262,140

Question

Quizplus · Accepted Answer

The sum of a geometric sequence can be calculated using the formula $ S_n = a \frac{r^n - 1}{r - 1} $. Here, $ a = 3 $, $ r = 4 $, and $ n = 8 $. Plugging in these values, $ S_8 = 3 \frac{4^8 - 1}{4 - 1} = 3 \frac{65536 - 1}{3} = 3 \times 21845 = 65,535 $.

Find the Sum of the Indicated Terms of the Geometric ∑n=1n=83(4)n−1\sum _ { n = 1 } ^ { n = 8 } 3 ( 4 ) ^ { n - 1 }n=1∑n=8​3(4)n−1

Find the Sum of the Indicated Terms of the Geometric $\sum _ { n = 1 } ^ { n = 8 } 3 ( 4 ) ^ { n - 1 }$