Write an equation for the nth term of the given geometric sequence. 12, 156, 2028, a

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!

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