The given sequence is 4, 16, 64, 256. To find the recursive rule, we first need to identify the common ratio between the terms.
We can see that:
- 16 / 4 = 4
- 64 / 16 = 4
- 256 / 64 = 4
Each term is obtained by multiplying the previous term by 4. Therefore, the common ratio (r) is 4.
To write the recursive rule, we need to express the nth term in terms of the (n-1)th term. The recursive rule can be stated as follows:
a1 = 4 (the first term is 4)
an = 4 * an-1 for n > 1 (each subsequent term is 4 times the previous term)
This way, you can generate the entire sequence from the first term.