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

Question

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

Options:

A . 16

B . 128

C . 240

D . 512

Answer: Option C

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

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

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