10% of 10=1,
20% 0f 20=4,
30% of 30=9,
40% of 40=16,........
90% 0f 90=81,
100% 0f 100=100,.....

Is it possible to create a similar series that gives us triangular numbers as the result?

I tried to prove this inductively, but I think it’s been a while since I did that kind of proof so I confused myself. However, I wonder if this will suffice:

I wanted to say that if I call the triangle numbers t1, t2, … tn then I have
10*n% of xn = tn
or
10*n/100 * xn = tn

tn = t[n-1] + n = n*(n+1)/2
xn = x[n-1] + 5 = 5*(n+1)   [since I said x1=10]

Well,
10*n/100 * xn = tn = n*(n+1)/2
10/100*xn = (n+1)/2
xn = 100/10*(n+1)/2
xn = 5*(n+1)

Does this count as a proof?

Similarly, Ady’s pattern follows:
5*n% of yn = tn
or
5*n/100 * yn = tn

tn = t[n-1] + n = n*(n+1)/2
yn = y[n-1] + 10 = 10*(n+1)   [since Ady said y1=20]

Well,
5*n/100 * yn = tn = n*(n+1)/2
5/100*yn = (n+1)/2
yn = 100/5*(n+1)/2
yn = 10*(n+1)