Prove using induction, that sequence is correct for all positive integers:

$a_{1}=1$
$a_{2}=4$
$a_{3}=12$

$a_{n}=4a_{n-1}-4a_{n-2}$

I would like you to show me the whole proof, I am learning now the elementary maths and I do not know how to prove it exactly by induction...

Sorry for my english...

2. Originally Posted by Ununuquantium
Prove using induction, that sequence is correct for all positive integers:

$a_{1}=1$
$a_{2}=4$
$a_{3}=12$

$a_{n}=4a_{n-1}-4a_{n-2}$

I would like you to show me the whole proof, I am learning now the elementary maths and I do not know how to prove it exactly by induction...

Sorry for my english...