Answer:
The recursive rule is an = (-4) · an-1
Explanation:
* Lets explain recursive formula for a geometric sequence:
1. Determine if the sequence is geometric (Do you multiply, or divide, the same amount from one term to the next?)
2. Find the common ratio. (The number you multiply or divide.)
3. Create a recursive formula by stating the first term, and then stating the formula to be the common ratio times the previous term.
# a1 = first term;
# an= r • an-1
- Where:
a1 = the first term in the sequence
an = the nth term in the sequence
an-1 = the term before the nth term
n = the term number
r = the common ratio
Ex: {3, 6, 12, 24, 48, 96, ...}
first term = 3, common ratio = 2
The recursive formula an = 2 · an-1
* In our problem:
- a1 = 4
- r = -16/4 = -4
- The recursive rule is
# an = (-4) · an-1