You basically have to think about what you have to do to the original 1,2,3,4,5...n to get to the answers in each sequence. So:
Sequence 1: 2,4,6,8,10 etc
To get from the original 1,2,3,4,5 you have to multiple each number in the original by 2 i.e. 2n
Sequence 2: 1,4,9,16,25 etc
To get from the original 1,2,3,4,5 you have to square each number in the original I.e. n2
Sequence 3: 4,9,14,19,24
To get from the original 1,2,3,4,5 you have to multiple each number in the original by 5 and subtract 1 I.e. 5n-1
So rather than thinking about the intervals you need to think what you do to each number in 1,2,3,4,5etc to get to the answers in the sequence.
Hope that makes sense...(and is right!).