I have a general question about recursion. When you're either evaluating a recursive definition like:

for

and trying to find a general formula for

or trying to give a recursive definition for a formula like:

Is there an easier way to do it then look at the sequence and try to find some pattern between the 2 formulas, because I'm really bad at figuring about patters in sequences and forming formulas from them.

Any help would be greatly appreciated. Thank you.