Question

Use inductive reasoning to predict the most probable next number in each list.

9, 13, 21, 33, 49, 69, ?

Answer 1

93

Explanation:

First differences increase by 4 each time. The given numbers are a quadratic sequence that can be described by 2n² -2n +9. The 7th term would be 93.

_____

First differences are ...

13-9 = 4, 21-13 = 8, 33-21 = 12, 49-33 = 16, 69-49 = 20

Second differences are ...

8-4 = 4, 12-8 = 4, 16-12 = 4, 20-16 = 4

When second differences are constant, the sequence can be represented by a second-degree polynomial function. The leading coefficient is half the value of the second differences.