So, today I was helping my cousin with his math homework, then I realized he had found the equation for a sequence of numbers taking the first index as 0 ... I never been so proud in my life.

It was wrong tho :(

I have a cousin who is in this same situation and I think it might be helpful if you could give some examples of what these sequences are and how do they compare to the other sequences.

It's really nice to see people taking care of their family and helping them with their homework. It's also really important that you are helping your cousin learn math. Although it sounds like you're doing a great job with that.