2025 SJI PRELIMS P1 Q11

The sequence begins \(T_1=1^2+1^2=2\), \(T_2=5^2+2^2=29\), \(T_3=9^2+3^2=90\), \(T_4=13^2+4^2=185\).

1. Evaluate \(T_5\).[1]
2. Find \(T_n\) in the form \(an^2+bn+c\), where \(a,b,c\) are integers.[3]