Induction, sequence, not hard, please help me

**Ununuquantium** · September 19th 2007, 10:53 AM

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...

Can anybody help me, please?

**CaptainBlack** · September 19th 2007, 11:57 AM

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...

Can anybody help me, please?

As stated there is nothing to prove as ststed, this is the definition of a sequence by a three term recurrence.

RonL

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