# Recursive definition??

• Jan 30th 2008, 01:04 AM
sfitz
Recursive definition??
I'm really sorry about how messy this looks; I'm still trying to figure out how to use the math notation thing.

Anyway, the problem is:

Given A0=1 and An+1=(3*An)+1, find the definition for An

I just have no idea how to go about doing this. You don't have to give the answer, just any sort of hint as to procedure would be great. Thank you!
• Jan 30th 2008, 01:37 AM
CaptainBlack
Quote:

Originally Posted by sfitz
I'm really sorry about how messy this looks; I'm still trying to figure out how to use the math notation thing.

Anyway, the problem is:

Given A0=1 and An+1=(3*An)+1, find the definition for An

I just have no idea how to go about doing this. You don't have to give the answer, just any sort of hint as to procedure would be great. Thank you!

$A_0=1$

$A_1=3 A_0+1=3+1$

$A_2=3 A_1+1=3^3 + 3 +1$

$A_3=3 A_2+1=3^3+3^2+3+1$

and so on..

RonL
• Jan 30th 2008, 02:25 AM
sfitz
Quote:

Originally Posted by CaptainBlack
$A_0=1$

$A_1=3 A_0+1=3+1$

$A_2=3 A_1+1=3^3 + 3 +1$

$A_3=3 A_2+1=3^3+3^2+3+1$

So I think I'm getting An=Sum from i=1 to n of $3^i$

That makes sense, because you multiply each previous term by 3, so there must be an exponent in there... haha, i think it's coming together in my head. Thank you!
• Jan 30th 2008, 02:37 AM
mr fantastic
Quote:

Originally Posted by sfitz
So I think I'm getting An=Sum from i=1 to n of $3^i$ Mr F says: No.

That makes sense, because you multiply each previous term by 3, so there must be an exponent in there... haha, i think it's coming together in my head. Thank you!

Close. But actually the sum will be from i = 0: $A_n = \sum_{i = 0}^n 3^i$.