SOLUTION: Please Help: Find the sum of the first five terms of the geometric sequence. a = 5, r = 4 A) 1715 B) 1704 C) 1701 D) 1705

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Question 201907: Please Help:
Find the sum of the first five terms of the geometric sequence.
a = 5, r = 4
A) 1715
B) 1704
C) 1701
D) 1705

Found 2 solutions by nerdybill, jim_thompson5910:
Answer by nerdybill(5413) About Me  (Show Source):
You can put this solution on YOUR website!
Find the sum of the first five terms of the geometric sequence.
a = 5, r = 4
A) 1715
B) 1704
C) 1701
D) 1705
.
5 + 5(4) + 5(4)(4) + 5(4)(4)(4) + 5(4)(4)(4)(4)
= 5 + 5(4) + 5(16) + 5(64) + 5(256)
= 5 + 20 + 80 + 320 + 1280
= 1705
.
Answer: D

Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
Here's an alternate method:

The formula for the sum of the first "n" terms of any geometric sequence is S=%28a%28r%5En-1%29%29%2F%28r-1%29




S=%28a%28r%5En-1%29%29%2F%28r-1%29 Start with the given formula


S=%285%284%5E5-1%29%29%2F%284-1%29 Plug in a=5, r=4, and n=5


S=%285%281024-1%29%29%2F%284-1%29 Raise 4 to the 5th power to get 1024


S=%285%281023%29%29%2F%283%29 Subtract


S=%285115%29%2F%283%29 Multiply


S=1705 Divide


So the sum of the first five terms is 1,705 which means that the answer is D)