Question

Find the nth term of this quadratic sequence
3, 8, 15, 24, 35

Answer 1

`a_n= (n+2)^2-1 =(n+3)(n+1)`

Explanation:

If you add 1 to each number, you get a perfect square: 4, 9, 16, 25, 36, which are the squares of 2, 3, 4, 5, 6...

`a_n= (n+2)^2-1 =(n+3)(n+1)`

Note that the two expressions are the same, but one might be more convenient than the other if you are manually calculating terms.