2025 CJC Promo Q1

A sequence \(T_n\) is given by \(T_n=\ln(n^a)+bn^2+c\) for \(n\in\mathbb{Z}^+\). The first three terms of the sequence are 9, 17.306 and 31.901.

1. Find the values of \(a\), \(b\) and \(c\), correct to the nearest integers.[3]
2. Using the integer values found in part (a), find the sum of the first hundred terms of \(T_n\).[1]