Question

Write a recursive formula;
4,12,36,108
Formula: an=a n-1
a1=4

Answer 1

a(n) = 3 a(n-1)
a(1) = 4

Answer 2

Just a little more detail on how we arrive at this:

n=1 a1=4=2^2
n=2, a2=12 = 3*4=3*2^2=3*a1
n=3, a3=36 = 3*12=3*3*4=3^2*2^2=3*a2
n=4, a4=108 = 3*36=3*3*12=3^2*3*4=3^3*2^2=3*a3

Pattern a1=4,an=3*a(n-1)

[Note also that any an can be found given an n using, an=3^(n-1) * 4 without knowing the previous value.]