The sum of first 45 natural numbers is:

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The sum of first 45 natural numbers is:

Options:

A . 1035

B . 1280

C . 2070

D . 2140

Answer: Option A

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

S_n =
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:

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

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