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### Discussion :: Numbers

1. The sum of first 45 natural numbers is

2.  A. 1035 B. 1280 C. 2070 D. 2140

Explanation :

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

sn=$${n\over2}$$[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:

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

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

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