Final answer:
The recursive formula for the given sequence is an = 0.8 * an-1, where a represents the nth term and an-1 represents the previous term.
Step-by-step explanation:
The given sequence 100, 80, 64, 51.2 follows a geometric pattern where each term is obtained by multiplying the previous term by a constant ratio. To find the recursive formula, we need to determine the common ratio.
To find the common ratio:
- Divide the second term (80) by the first term (100): 80/100 = 0.8
- Divide the third term (64) by the second term (80): 64/80 = 0.8
- Divide the fourth term (51.2) by the third term (64): 51.2/64 = 0.8
Since the common ratio is consistent at 0.8, we can write the recursive formula as:
an = 0.8 * an-1
where a represents the nth term in the sequence and an-1 represents the previous term.