To find the next three terms in the sequence 3, 12, 21, we first need to identify the pattern that the numbers follow.
Let’s look at the differences between the terms:
- The difference between 12 and 3 is: 12 – 3 = 9
- The difference between 21 and 12 is: 21 – 12 = 9
We can see that the difference between consecutive terms is consistent, with a difference of 9. This suggests that the sequence is an arithmetic progression (AP) where each term increases by a fixed number.
To find the next term following 21, we add 9:
- 21 + 9 = 30
The next term is 30.
Continuing this pattern:
- 30 + 9 = 39
- 39 + 9 = 48
Thus, the next three terms in the sequence after 3, 12, and 21 are: 30, 39, and 48.