Originally Posted by

**Kevmck** I'm not sure I fully understand how to do a recursive definition for an integer sequence containing an exponent.

$\displaystyle a_n = 4^n + 12; \forall n \geq 0$

I can figure out that:

$\displaystyle 4^0 + 12 = 13$

$\displaystyle 4^1 + 12 = 16$

$\displaystyle 4^2 + 12 = 28$

$\displaystyle 4^3 + 12 = 76$

$\displaystyle 4^4 + 12 = 268$

which equates to (mutiples of 4) x 12...but I'm not sure how to finish this to make it a recursive definition. The question I'm trying to answer has different values, my hope is to learn how to do this in general and not the specific question I'm required to answer.