[Discrete Mathematics] For {1,3,6,10,15,…}. Find a recursive formula.

Let $a_n$ be the $n^{th}$ term. Then with $a_1=1$, and we can verify that 
\[a_{n}=a_{n-1}+n, \ \ \ \ n\geq 2.\]
This is the recursive formula for the stated sequence. You can check that
\[a_2=1+2=3, a_3=3+3=5, a_4=5+5=10, a_5=10+5=15, \dots .\]