Find an equation for the nth term of the sequence.
-1, -4, -16, -64
a. an = -1 • 4^n - 1
b. an = -1 • 4^n
c. an = 4 • -1^n
d. an = 4 • -1^n + 1

a. an = -1 • 4^(n - 1)

Step-by-step explanation:

It's easy see that each term is multiplied by 4 to get the next term, so the common ratio will be 4, that reduces the choices to answers A and B (since C and D use -1 as common ratio).  Also, normally a geometric progression uses "n-1", so we'll first try with A to see if it works.

a1 = (-1) * 4^0 = -1 * 1 = -1

a2 = (-1) * 4^1 = -1 * 4 = -4

a3 = (-1) * 4^2 = -1 * 16 = -16

Yes, it works... so the answer is an = -1 • 4^(n - 1)

correct answer:

i^31 = -i