geometry
posted by jill .
describe a pattern in the numbers 4,6,9,13,18

They are monotonically increasing.
They are increasing a distance of n apart, as in
1st, 2nd, 3rd, 4th, 5th, 6th, ...nth
4, 4+2, 6+3, 9+4, 13+5, 18+6, ...(n1 term)+n 
or
term(1) = 4
term(2) = 6
term(3) = term(1) + term(2)  1 = 9
term(4) = term(2) + term(3)  2 = 13
term(5) = term(3) + term(4)  3 = 18
...
term(n) + term(n2) + term(n1)  (n2)
this is called a recursive formula,
or
term(n) = n(n+1)/2 + 3
Including bobpursley's pattern , there are probably some more 
Describe a pattern in the numbers: 4, 6, 9, 13, 18