Question

Exercise 4.X3 Make a reasonable conjecture about the nth term in the sequence. 5 9 15 23 33

Answer 1

Conjecture: next term is 45

Explanation:

One very common sequence is one where the difference between one term and the previous one follows a recognizable pattern. Let's inspect the difference from one term to the previous one in the sequence:

Difference from 9 to 5: 9 - 5 = 4

Difference from 15 to 9: 15 - 9 = 6

Difference from 23 to 15: 23 -15 = 8

Difference from 33 to 23: 33-23= 10

At this point the pattern is clear, the differences are just even numbers increasing 2 by 2. We would expect next difference to be 12, and so the next term on the sequence should be 33 + 12 = 45.