The sum all even natural numbers between 1 and 31 is:

Required sum = (2 + 4 + 6 + ... + 30)

This is an A.P. in which a = 2, d = (4 - 2) = 2 and l = 30.

Let the number of terms be n. Then,

t_n = 30 ⟹    a + (n - 1)d = 30

⟹ 2 + (n - 1) x 2 = 30

⟹ n - 1 = 14

⟹ n = 15

∴Sn =	n	(a + l)	=	15	x (2 + 30)   = 240.
	2			2