Use a graphing utility to find the sum of the geometric sequence. Round answer to two decimal places, if necessary.
-$$\sum _ { k = 1 } ^ { 5 } 4 ( 3 ) ^ { k }$$
A) 93
B) 480
C) 2,460
D) 1,452

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} $, where $ a = 4 $, $ r = 3 $, and $ n = 5 $. Plugging in these values gives $ S_5 = 4 \frac{3^5 - 1}{3 - 1} = 4 \frac{243 - 1}{2} = 4 \times 121 = 484 $. However, the sequence starts at $ k=1 $, so we need to calculate $ 4 \times 3^1 + 4 \times 3^2 + 4 \times 3^3 + 4 \times 3^4 + 4 \times 3^5 = 12 + 36 + 108 + 324 + 972 = 1452 $.

Use a Graphing Utility to Find the Sum of the Geometric