Sequence 4,16,36,64,100

This is a quadratic sequence.

16-4=12 and 36-16=20

20-12=8

there is a common difference of 8, so you add 12 to the first term to get the second term, that means you will add 8+12=20 to the second term to get the third term, then you will add 8+20=28 to the third term to get the fourth term, and so on ... it's called a common difference.

so

2nd term: 4+12=16

3rd term: 16 + (8+12) = 16 + (20) = 36

4th term: 36 + (8+20) = 36 + (28) = 64

5th term: 64 + (8+28) = 64 + (36) = 100

If you're looking for the rule, it's: they're all even squared numbers

i. e. 2^2 = 4, 4^4 = 16, etc.

if you're looking for more numbers, three more are: 12^12 = 144, 14^14 = 196, 16^16 = 256