This kind of thing is also a killer to me too.
deteq did it right.
(1/2) [n(n+1)] for 1,3,6,10,15
for 3,6,10,15,21 it's almost the same except the numbers have
grown by 2,3,4,5,6
n1+a = 2
n2+a = 3 ...
a = 1
so (1/2) [n(n+1)]+n+1 is the answer. I merely expanded on his
answer.