Q1: The sum of first 45 natural numbers is:

ANS:A - 1035

Let S_n =(1 + 2 + 3 + ... + 45). This is an A.P. in which a =1, d =1, n = 45.

Sn =	n	[2a + (n - 1)d]	=	45	x [2 x 1 + (45 - 1) x 1]	=		45	x 46		= (45 x 23)
	2			2				2

= 45 x (20 + 3) = 45 x 20 + 45 x 3 = 900 + 135 = 1035. Shorcut Method:

Sn =	n(n + 1)	=	45(45 + 1)	= 1035.
	2		2