Question

describe a pattern in the numbers 4,6,9,13,18

Answer 1

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, ...(n-1 term)+n

Answer 2

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(n-2) + term(n-1) - (n-2)

this is called a recursive formula,

or

term(n) = n(n+1)/2 + 3

Including bobpursley's pattern , there are probably some more

Answer 3

Describe a pattern in the numbers: 4, 6, 9, 13, 18