MATH SOLVE

4 months ago

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

Accepted Solution

A:

Answer:Conjecture: next term is 45Step-by-step 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 = 4Difference from 15 to 9: 15 - 9 = 6Difference from 23 to 15: 23 -15 = 8Difference from 33 to 23: 33-23= 10At 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.