SOLUTION: Find the sum of the first n terms of each geometric sequence. S sub 6 ; 1 + 4 + 16 + 64 + ...

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Question 979194: Find the sum of the first n terms of each geometric sequence.
S sub 6 ; 1 + 4 + 16 + 64 + ...
Answer by ikleyn(52817) About Me  (Show Source):
You can put this solution on YOUR website!

The first term of this geometric progression  a%5B1%5D = 1,   and the ratio is  q = 4.

The formula for the sum of first  n  terms of a geometric progression is

S%5Bn%5D = %28a%5B1%5D%2A%28q%5En-1%29%29%2F%28q-1%29

(see everythere,  for example,  in the lesson  Geometric progressions  in this site).
Substitute here  a%5B1%5D=1,  q=4  and   n=6,   and you will get

S%5B6%5D = %284%5E6-1%29%2F%284-1%29 = %284%5E3-1%29%2A%284%5E3%2B1%29%2F3 = %2864-1%29%2A%2864%2B1%29%2F3 = %2863%2A65%29%2F3 = 21*65 = 1365 .