SOLUTION: The sum of first 6 terms of the geometric sequence is 1,-2,4,-8,....is?

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Question 978567: The sum of first 6 terms of the geometric sequence is 1,-2,4,-8,....is?
Answer by ikleyn(52788) 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 = -2.

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  and   n=6,   and you will get

S%5B6%5D = %281%2A%28%28-2%29%5En-1%29%29%2F%28-2-1%29 = %28%28-1%29%5En%2A2%5En-1%29%2F%28-3%29 = %281-%28-1%29%5En%2A2%5En%29%2F3 = %281+-+%28-1%29%5E6%2A2%5E6%29%2F3 = %281+-+2%5E6%29%2F3 = %281-64%29%2F3 = -63%2F3 = -21.