SOLUTION: How to find An and n if Sn,A1 and d is given?

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Question 956360: How to find An and n if Sn,A1 and d is given?
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
Start with this sum formula for an arithmetic sequence:

S%5Bn%5D=expr%28n%2F2%29%282a%5B1%5D%2B%28n-1%29%5E%22%22d%29

Substitute Sn, a1 and d in this formula
and solve.  It should factor if there is a solution.  

Using the letters and the quadratic formula, I got this:

n+=+%28d-a%5B1%5D+%2B-+sqrt%28%28a%5B1%5D-d%29%5E2%2B8dS%5Bn%5D%29%29%2F%282d%29

At least one of those two solutions (using either the + or the -) 
will give a positive whole number for n, if there is a solution.

Then substitute that value of n along with a1 and d
into the general term formula:

a%5Bn%5D=a%5B1%5D%2B%28n-1%29d  

In some cases there may be two solutions.

Edwin