Question

Nth term quadratic sequence ??

Answer 1

Tn = n^2 + 2n + 9.

Explanation:

12 17 24 33 44 57 72...

Differences 5 7 9 11 13 15

Differences 2 2 2 2 2

The value of 2 indicates that the first term is n^2.

T 12 17 24 33

n 1 2 3 4

n^2 : 1 4 9 16

T - n^2 11 13 15 17

this last sequence has Tn = 11 + 2(n - 1) = 2n + 9.

So the nth term of the quadratic sequence is n^2 + 2n + 9.