Induction for sequences

**qtpipi** · February 26th 2009, 10:16 PM

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

**arpitagarwal82** · February 26th 2009, 10:23 PM

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.

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