# Math Help - Induction for sequences

1. ## Induction for sequences

OK, I am completely stupid when it comes to induction. Any help? I shouldn't have taken this class.

2. Use Mathematicla induction for part 1.
let $S_n$be a statement that $a_n$ is odd

Assume $S_{k-2}$ and $S_{k-1}$ are true and then prove $S_k$is true.

$a_k = 2a_{k-2} +3a_{k-1}$

Now $2a_{k-2}$ is even and $3a_{k-1}$ is odd since odd multiplied by odd is odd.

Sum of an even number and odd number is always odd.
so $a_k$is odd.
Hence $S_k$ is proved true.

base case $a_1$ and $a_2$are already give odd.