SOLUTION: the sum of n terms of an arithmetic series is:Sn=5n^2-11. Determine common difference

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Question 1070612: the sum of n terms of an arithmetic series is:Sn=5n^2-11. Determine common difference
Answer by KMST(5328)   (Show Source): You can put this solution on YOUR website!
There is a typo there.
cannot be the sum of n terms of an arithmetic series,
but could be .
You could use either expression to find the common difference ,
but only a sum of the form could work to find an actual
arithmetic series, with a first term independent of .

A WAY TO SOLVE IT WITH :
The sum of terms is




and since where is term number ,
we can find an expression for .





That gives us as the common difference,
and as the first term.
We know that in an arithmetic sequence
with a first term ,
and a common difference ,
term number is
,
so is the coefficient of ,
and the other term is .

WHY WE KNOW IS WRONG:
We have the "formula"
In that expression is a factor.
The expression is a quadratic (degree 2) polynomial with



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