Question

What are the next 2 numbers in the pattern 1, 4, 9, 16, 25, 36, 49, . . .

Answer 1

the next two numbers would be 64 and 82

1+3=4
4+5=9
9+7=16
16+9=25
25+11=36
36+13=49
Hope that you see the pattern here

Answer 2

This pattern is adding the next odd number, starting with 3. For example, we can use the first few numbers:
1 + 3 = 4
4 + 5 = 9
9 + 7 = 16

This means that when we reach 49, we have to add 17 into it to get the answer of 66.