# Proof By Strong Induction Questions, Answers and Solutions

a - answer    s - solution    v - video    d - discussion

## Question 1

Prove:

a) $T_n=3^n-2^n$ if $T_{n+2}=5T_{n+1}-6T_n$, $T_1=1$, $T_2=5$ for all $n\ge3$ and $n\in\mathbb{Z}^+$a s v d

b) $T_n=3\times2^{n-1}+2(-1)^n$ if $T_{n}=T_{n-1}+2T_{n-2}$, $T_1=1$, $T_2=8$ for all $n\ge3$ and $n\in\mathbb{Z}^+$a s v d