Answer:
3x^2 + 3 --> 6, 15, 30, 51
2x^2 - 1 --> 1, 7, 17, 31
x^2 + 2 --> 3, 6, 11, 18
Explanation:
Let's start with the first equation; 3x^2 + 3
Substitute 1 (the first digit in a sequence) for x.
3(1^2) + 3
3(1) + 3
3 + 3 = 6
3(2^2) + 3 Then the second digit.
3(4) + 3
12 + 3 = 15
Since the two numbers we have so far are 6 and 15, there is only one sequence this could match. 6, 15, 30, 51.
2(1^2) - 1
2(1) - 1
2 - 1 = 1
This equation represents 1, 7, 17, 31.
These same steps apply to the other equation as well.
1^2 + 2, then 2^2 + 2, then 2^2 + 2, and so on. (But we don't need to do extra work to figure that out.)