1.  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)
2 2

= (15 x 16) = 240.