SOLUTION: the sum of the first n terms of a series is given by Sn=n^2+2n .Find the rth term and the first three terms of the series.

Question 1194991: the sum of the first n terms of a series is given by Sn=n^2+2n .Find the rth term and the first three terms of the series.
Answer by ikleyn(52788) (Show Source): You can put this solution on YOUR website!
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the sum of the first n terms of a series is given by Sn=n^2+2n .
Find the rth term and the first three terms of the series.
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I will explain you how to derive the formula for the n-th term  .



Notice (and it is OBVIOUS) that   =  - .


Substitute here the formulas for    and  

     = -  =  - 


and simplify it

               =  = 2n + 1.


Thus the formula for the n-th term is

     = 2n + 1,  n = 1, 2, 3, 4, 5, . . . 


To get first 3 term, substitute n= 1, 2, 3 into this formula and calculate

     = 3;    = 5;   = 7.

Solved and clearly explained.

Let me know if any point of my explanation is clear to you . . .

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