SOLUTION: 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, ...}

Algebra ->  Radicals -> SOLUTION: 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, ...}      Log On


   

Question 1068918: 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 by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
looks like each succeeding number is 4 times the preceding number and the sign is changed.

-4 * -3 = 12
12 * -3 = -36

if -4 is the nth term in the sequnce, then the (n+1)th term is equal to -3 * that.

if 12 is the nth term in the sequence, then the (n+1)th term is equal to -3 * that.

the recursive formula would then be A[n+1] = A[n] * -3

A[n+1] is the (n+1)th term.
A[n] is the nth term.

if you start with A1 = -4, then:
A2 = A1 * -3 = -4 * -3 = 12
A3 = A2 * -3 = 12 * -3 = -36
A4 = A3 * -3 = -36 * 108
A5 = A4 * -3 = 108 * -3 = -324