Number of red circle shapes used in the patteren :

Question

3 , 6 , 10

The first difference is +3 and + 4
which leads the second difference to be +1

What do I do after this? especially if the 1st difference is 1?

Answer 1

I expect the differences are 3,4,5,6,7,...

Did you know that 1+2+3+...+n = n(n-1)/2 ?

Answer 2

sorry, that's n(n+1)/2

So, you have (n+1)(n+2)/2

Answer 3

Yes , but how do you get
n(n+1)/2?

How do you do the working to achieve it?
because normally you 1/2 the second difference and square the numbers to get a new sequence and then subtract the new sequence from 3 , 6 , 10.