Final answer:
The pattern in the sequence is found by identifying the differences between successive terms, which are increasing by 2. The next two numbers in the sequence are 30 and 42.
Step-by-step explanation:
To find the pattern in the sequence 0, 2, 6, 12, 20, we look for the differences between successive terms. We can calculate these differences:
- 2 - 0 = 2
- 6 - 2 = 4
- 12 - 6 = 6
- 20 - 12 = 8
We see that the differences are increasing by 2 each time. If we continue this pattern, the next difference would be 10 (8 + 2), so the next number in the sequence is 20 + 10 = 30.
Continuing this further, the following difference would be 12 (10 + 2), giving us the number after 30 as 30 + 12 = 42.
Therefore, the next two numbers in the sequence are 30 and 42.