Find the sum of the geometric series.
-$$\sum _ { i = 1 } ^ { 5 } 4 ( 3 ) ^ { i }$$
A) 1452
B) 2460
C) 480
D) 93

Question

Quizplus · Accepted Answer

The series is a geometric series with the first term $ a = 4 \times 3 = 12 $ and common ratio $ r = 3 $. The sum of the first $ n $ terms of a geometric series is given by $ S_n = a \frac{r^n - 1}{r - 1} $. Substituting $ a = 12 $, $ r = 3 $, and $ n = 5 $, we get $ S_5 = 12 \frac{3^5 - 1}{3 - 1} = 12 \times \frac{243 - 1}{2} = 12 \times 121 = 1452 $.

Find the Sum of the Geometric Series ∑i=154(3)i\sum _ { i = 1 } ^ { 5 } 4 ( 3 ) ^ { i }i=1∑5​4(3)i

Find the Sum of the Geometric Series $\sum _ { i = 1 } ^ { 5 } 4 ( 3 ) ^ { i }$