SOLUTION: The sum of how many terms of the series 3,-6,12, ....will be 513?

Algebra ->  Sequences-and-series -> SOLUTION: The sum of how many terms of the series 3,-6,12, ....will be 513?      Log On


   

Question 891783: The sum of how many terms of the series 3,-6,12, ....will be 513?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
That looks like geometric sequence, r=-2.
The general sequence's term is 3%2A%28-2%29%5E%28n-1%29 and n would be the index of the term.

You can think of the sequence this way:
3, 3(-2)^1, 3(-2)^2, 3(-2)^3, 3(-2)^4,....3(-2)^n
This way showing the sequence uses indexing from 0 to n-1.
Sum of the first n terms is highlight%283%28%281-%28-2%29%5En%29%2F%281-%28-2%29%29%29%29.
For reference, other than a good college algebra book, you can see http://en.wikipedia.org/wiki/Geometric_series.