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Numbers

Q1: The sum all even natural numbers between 1 and 31 is:

A 16

B 128

C 240

D 512

ANS:C - 240

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.
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