SOLUTION: Given a4=35 and s14=931, find the common difference d and a1.

Algebra.Com
Question 978276: Given a4=35 and s14=931, find the common difference d and a1.
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!
[You did not give enough information.  You had this:
an=35 and s14=931 a sub n ,common diffence and a sub 1
However I guessed that a4=35 was given, and rewrote your question as above.]

We use the nth term formula:



Substitute n=4, then a4=35





We use the sum formula:



Substitute n=14, then S14=931





Both sides can be divided through by 7:



So now we have this system of equations:



Solve that and get a1=8, d=8.

If my guess of a4=35 is correct, then your sequence was

8, 17, 26, 35, 44, 53, 62, 71, 80, 89, 98, 107, 116, 125 

That sequence of 14 terms does have sum 931.

If I guessed wrong, then you can use the above as a guide.

Edwin
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