Answer:
a(n) = 12 * (13)^(n-1)
Step-by-step explanation:
First step is to determine what's the scale/multiplication factor between each term:
156 / 12 = 13
2028 / 156 = 13
So, since we got 13 between 1st, 2nd and 3rd term, we can be confident it's the right multiplication factor.
an would be the first term (12) multiplied by a factor of 13. So,
If we try for n > 1, we have
a(2) = 12 * (13)^(2-1) = 12 * 13 = 156
a(3) = 12 * (13)^(3-1) = 12 * 13² = 12 * 169 = 2028
It matches!