Question

An arithmetic sequence is represented as 5 , 9 , 13 , ... with the nth term represented as 4n + 1. Write a formula to represent the sum of the first n terms.

Answer 1

Let
`a_n=4n+1`.


`S_n=\displaystyle\sum_(k=1)^na_k=\sum_(k=1)^n(4k+1)`

`S_n=\displaystyle4\sum_(k=1)^nk+\sum_(k=1)^n1`

`S_n=\displaystyle4\frac{n(n+1)}2+n`

`S_n=2n^2+3n`