1. 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!

2. 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!
$\displaystyle A_0=1$

$\displaystyle A_1=3 A_0+1=3+1$

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

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

and so on..

RonL

3. Originally Posted by CaptainBlack
$\displaystyle A_0=1$

$\displaystyle A_1=3 A_0+1=3+1$

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

$\displaystyle A_3=3 A_2+1=3^3+3^2+3+1$
So I think I'm getting An=Sum from i=1 to n of $\displaystyle 3^i$

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!

4. Originally Posted by sfitz
So I think I'm getting An=Sum from i=1 to n of $\displaystyle 3^i$ 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: $\displaystyle A_n = \sum_{i = 0}^n 3^i$.