Question 107853: Could someone please explain to me how to find an algebraic expression to calculate the nth term of the following sequence?:
2, 5, 11, 23, 47, 95, 191
I know that the equation to continue the series is 2x+1, but I've tried for 2 hours to figure out an equation for the nth term, and all I've gotten is frustrated!
Thanks so much for any help!!
Found 2 solutions by checkley71, scott8148:
Answer by checkley71(8403)   (Show Source):
You can put this solution on YOUR website! THE FORMULA FOR FINDING THE Nth TERM OF A GEOMETRIC SERIES IS:
An=AR^(n-1) A IS THE FIRST TERM, n IS THE TERM TO BE FOUND & R IS THE RATIO:
IN YOUR CASE THE RATIO IS (2X+1).
Answer by scott8148(6628)  (Show Source):
You can put this solution on YOUR website! look at the differences between terms ... 3, 6, 12, 24, 48, 96
... the difference is doubling, so 2 is being raised to a sequential power
look at the terms ... 3-1, 3*2-1, 3*4-1, 3*8-1, 3*16-1, etc.
... 3*(2^0)-1, 3*(2^1)-1, 3*(2^2)-1, 3*(2^3)-1, etc.
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