Answer:
Tn = n^2 + 2n + 9.
Step-by-step 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.
