Find the sum of the finite geometric sequence.Round to the nearest thousandth. $\sum _ { i = 0 } ^ { 5 } 600 ( 1.05 ) ^ { i }$
A)4081.148
B)3197.686
C)4285.205
D)3481.148
E)3315.379

Question

Quizplus · Accepted Answer

The sum of a finite geometric sequence is given by the formula:$$S_n = a(1 - r^n) / (1 - r)$$where a is the first term, r is the common ratio, and n is the number of terms.In this case, a = 600, r = 1.05, and n = 6.Plugging these values into the formula, we get:$$S_6 = 600(1 - 1.05^6) / (1 - 1.05)$$$$S_6 = 600(1 - 1.2762815625) / (1 - 1.05)$$$$S_6 = 600(0.2762815625) / (0.05)$$$$S_6 = 4081.148$$Therefore, the sum of the finite geometric sequence is 4081.148, rounded to the nearest thousandth.

Find the Sum of the Finite Geometric Sequence ∑i=05600(1.05)i\sum _ { i = 0 } ^ { 5 } 600 ( 1.05 ) ^ { i }∑i=05​600(1.05)i

Find the Sum of the Finite Geometric Sequence $\sum _ { i = 0 } ^ { 5 } 600 ( 1.05 ) ^ { i }$