Final answer:
The rule for the given sequence is obtained by multiplying the previous term by 5 and then subtracting 4.
Step-by-step explanation:
The rule for the given sequence 3, 17, 87, 437, ... is as follows: each term in the sequence is obtained by multiplying the previous term by 5 and then subtracting 4.
Let's see how this rule applies to the sequence:
3 x 5 - 4 = 17
17 x 5 - 4 = 87
87 x 5 - 4 = 437
Therefore, the next term in the sequence would be obtained by multiplying 437 by 5 and subtracting 4, resulting in 2183. So the next term is 2183.