2025 PHS PRELIMS P1 Q19

The first terms of a sequence are \(T_1=2^0+1\), \(T_2=2^1+3\), \(T_3=2^2+5\), and \(T_4=2^3+7\).

1. Write down \(T_5\).[1]
2. Express \(T_n\) in terms of \(n\).[2]
3. Hence show that \(T_n-T_{n-1}=2^{n-2}+2\).[2]