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

Answer 1

Since it is a geometric sequence, you know that there should be a ratio between every pair of consecutive terms.

Let's consider -4 and 12, the first two terms of the sequence.

-4 × r = 12

r = -3

Thus the every term is -3 times the last term.

To confirm this is correct, consider the second two terms, 12 and -36.

12 × -3 = -36

-36 = -36 Great!

Then the recursive formula must be a_n = -3 × a_n-1.

Following -36, the 4th term must be -3 × -36 = 108.

Then the 5th term would be -3 × 108 = -324.