Numbers - Arithmetic Aptitude Questions and Answers

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The sum of first 45 natural numbers is

1035

1280

2070

2140

Answer : Option A

Explanation :

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

s_n= ${n\over2}$ [2a + (n - 1)d]= ${45\over 2}$ $\times$ [2 $\times$ 1+(45-1) $\times$ 1]=[ ${45 {} \over 2}$ $\times$ 46]=(45 $\times$ 23)

= 45 x (20 + 3)

= 45 x 20 + 45 x 3

= 900 + 135

= 1035.

Shorcut Method:

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

s_{n= ${n(n+1) \ \over 2}$ = ${45(45+1) \over 2}$ =1035}

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