SOLUTION: find the sum -1+3+7+...+(4n-5) This is calculus

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Question 1104778: find the sum -1+3+7+...+(4n-5)
This is calculus
Answer by greenestamps(13216) About Me  (Show Source):
You can put this solution on YOUR website!


Again... no, this is not calculus.

This is an arithmetic series with first term -1 and common difference 4.

The sum of the terms of an arithmetic series can be calculated as (number of terms) times (average of first and last terms).

To find the number of terms in the series,
(1) find the difference between the last and first terms;
(2) divide that difference by the common difference between terms; and
(3) add 1 (because steps (1) and (2) found the number of terms AFTER the first term)

%284n-5%29-%28-1%29+=+4n-4
%284n-4%29%2F4+=+n-1

The average of the first and last terms is %28%28-1%29%2B%284n-5%29%29%2F2+=+2n-2
So the sum of the series is %28n-1%29%282n-2%29+=+2%28n-1%29%5E2