what is the next number in the pattern: 3,4,6,9,13,18,24,___

31 3 + 1 = 4

4 + 2 = 6
6 + 3 = 9
9 + 4 = 13

Do you see the pattern?

39,48

after the 31 its 39,48

To find the next number in the pattern, let's analyze the differences between adjacent terms.

The first difference between the numbers is: 4 - 3 = 1
The second difference is: 6 - 4 = 2
The third difference is: 9 - 6 = 3
The fourth difference is: 13 - 9 = 4
The fifth difference is: 18 - 13 = 5
The sixth difference is: 24 - 18 = 6

By observing these differences, we can see that the differences themselves form a pattern: 1, 2, 3, 4, 5, 6. These are consecutive natural numbers.

To find the next difference, we can add 7 (the next natural number) to the last difference: 6 + 7 = 13.

Now, to find the next number in the sequence, we add this new difference to the last number: 24 + 13 = 37.

Therefore, the next number in the pattern is 37.