a1=10,
a2-a1=5,
a3-a2=6
a4-a3=7
a5-a4=8
an-a(n-1)=3+n
an-a1=5+6+7+...(n+3) = (n+8)*(n-1)/2
an=10+(n^2+7n-8)/2= (n^2+7n+12)/2=(n+3)(n+4)/2