Question

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 1

S(n) = n^2 + 2n
S(1) = 1^2 + 2(1) = 3
S(2) = 2^2 + 2(2) = 8
S(3) = 3^2 + 2(3) = 15
...

Sum of 1 term is 3. Therefore, the first term in the series is: 3
Sum of the first two terms = S(2) = 8. Subtract first term from above to get the second term: 8 - 3 = 5.
Sum of the first three terms = S(3) = 15. Subtract sum of first two terms, S(2), to get the third term: 15 - 8 = 7

So the series is: 3 + 5 + 7 + .....

What is the rth term of the above series?