SOLUTION: The sum of the first n terms of an arithmetic sequence is (2n^2)-n. Find the general term and show that the sequence is an arithmetic sequence

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Question 1011566: The sum of the first n terms of an arithmetic sequence is (2n^2)-n. Find the general term and show that the sequence is an arithmetic sequence
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
To find the sum of the first n terms of an arithmetic sequence use the formula,

S%5Bn%5D=+n%28a%5B1%5D%2Ba%5Bn%5D%29%2F2

if S%5Bn%5D=%282n%5E2%29-n, we have

%282n%5E2%29-n=+n%28a%5B1%5D%2Ba%5Bn%5D%29%2F2....solve for the general term a%5Bn%5D

2%282n%5E2-n%29%2Fn=+a%5B1%5D%2Ba%5Bn%5D

2n%282n-1%29%2Fn=+a%5B1%5D%2Ba%5Bn%5D

2%282n-1%29=+a%5B1%5D%2Ba%5Bn%5D

a%5Bn%5D=2%282n-1%29-+a%5B1%5D