To find the next number in the series 2, 5, 11, 20, 32, 47, let’s first look at the differences between consecutive terms:
- 5 – 2 = 3
- 11 – 5 = 6
- 20 – 11 = 9
- 32 – 20 = 12
- 47 – 32 = 15
So, the differences are: 3, 6, 9, 12, 15. We can see that the differences themselves form an arithmetic series where each term increases by 3.
If we continue this pattern, the next difference after 15 would be 15 + 3 = 18.
Now, we can add this next difference to the last number in our original series:
47 + 18 = 65.
Therefore, the next number in the series is 65.