To find the next number in the series 2, 5, 11, 20, 32, 47, let’s first examine the differences between consecutive numbers:
- 5 – 2 = 3
- 11 – 5 = 6
- 20 – 11 = 9
- 32 – 20 = 12
- 47 – 32 = 15
Here are the differences:
- 3
- 6
- 9
- 12
- 15
Next, we can see that these differences are increasing by 3 each time:
- 6 – 3 = 3
- 9 – 6 = 3
- 12 – 9 = 3
- 15 – 12 = 3
Continuing this pattern, the next difference should be:
- 15 + 3 = 18
Now, we’ll add this difference to the last number in the original series:
- 47 + 18 = 65
Therefore, the next number in the series is 65.