SOLUTION: In the arithmetic series, if S_n = 5n^2+4n, find the first three terms. So the first term is 9, and I tried using the formula S_n= (a1+an)/2 * n I got confused... does an = 5

Question 1106491: In the arithmetic series, if S_n = 5n^2+4n, find the first three terms.
So the first term is 9, and I tried using the formula S_n= (a1+an)/2 * n
I got confused... does an = 5n^2+4n
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52788)   (Show Source): You can put this solution on YOUR website!
.

The first term is = 9 with n = 1. The second term is - = 28-9 = 19. The third term is - = 57-28 = 29. That is all you need. The first three terms are 9, 19 and 29.

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    - The proofs of the formulas for arithmetic progressions
    - Problems on arithmetic progressions
    - Word problems on arithmetic progressions

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Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

The sum of n terms of an arithmetic series is

(number of terms) times (average of first and last terms)

If the first term is a and the common difference is d, then the sum of the first and last terms is

and the sum of the first n terms is then

We are told that the sum of the first n terms of the sequence is 5n^2+4n. So

This tells us
which means d is 10, and

So the arithmetic series has first term 9 and common difference 10.

Then the first three terms are 9, 19, and 29.
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