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

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

[A].

16

[B].

128

[C].

240

[D].

512

Answer: Option C

Explanation:

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,

tn = 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