Question

For the following geometric sequence find the recursive formula and the 5th term in the sequence. In your final answer, explain. {-4, 12, -36, ...}

Answer 1

you have to multiply by -3

so the answers are going to be one negative one positive

and the next 5th terms are 108,-324,972,-2916,8748

Answer 2

12 / -4 = -3, also -36 / 12 = -3.

So the sequence goes:

-4, -4(-3), -4(-3)(-3), ... or -4, -4(-3), -4(-3)^2...

So the recursive formula to find any term would be -4(-3)^n, where n = 0 for the first term.

So for the 5th term, n = 4 and so:
-4(-3)^4 = -324.

You can check as it would be -36 * -3 * -3 = -36*9 = -324.