[1035] The sum of first 45 natural numbers is:

For Competitive Exams

The sum of first 45 natural numbers is:

1035

1280

2070

2140

Explanation:

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

S_n =$ \dfrac{n}{2} $[2$ a $ + $\left( n - 1\right)$ d ]=$ \dfrac{45}{2} $ x [2 x 1 + (45 - 1) x 1]=$ \dfrac{45}{2} $x 46= 45 x 23

= 45 x (20 + 3)

= 45 x 20 + 45 x 3

= 900 + 135

= 1035.

Shorcut Method:

S_n =$ \dfrac{n(n + 1)}{2} $=$ \dfrac{45(45 + 1)}{2} $= 1035.

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