Aptitude - Numbers - Discussion

Discussion :: Numbers - General Questions (Q.No.20)

20. 

The sum of first 45 natural numbers is:

[A]. 1035
[B]. 1280
[C]. 2070
[D]. 2140

Answer: Option A

Explanation:

Let Sn =(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


Bill said: (Apr 14, 2011)  
Help me to find even more easy way.

K.Pavan said: (May 31, 2012)  
n/2 * (a+L) where L is the last term that is 45.a is the first term that is 1. since natural numbers start from 1

Puneet said: (Jun 9, 2013)  
[N/2]*(first term + last term).

Rohit Singla said: (Nov 14, 2014)  
Middle no.of 45 is 23.
So its average is also 23.

23*45 = 1035.

Piyosh said: (Jan 16, 2016)  
Is this n(n+1)/2 applicable for all A.P?

Smiley said: (Jun 22, 2016)  
Does the shortcut method work in every case?

Rohan said: (Jul 1, 2016)  
@Rohit, I like your method quit interesting.

Vinayak said: (Jul 9, 2016)  
@Rohit.

I like your method it's a simple thing to get an answer.

Bimal said: (Jul 28, 2016)  
Sum upto nth of natural numbers = n* (n + 1)/2,

Put n = 45 here.

Manali said: (Nov 9, 2016)  
Simplest way to multiply the given number with its consecutive number and then divide by 2.
i.e (45 * 46)/2 = 1035.

Tohid said: (Jun 3, 2017)  
n(n + 1)÷2 = 45(45 + 1)÷2 = 1035.

Rinkal said: (Dec 12, 2017)  
I like your method, thanks @Rohit.

Jignesh said: (Jan 4, 2018)  
Good method @Rohit.

Md Ikramul Haque said: (Jul 24, 2018)  
4+5=9.
And 1035=1+0+3+5=9.
Answer is A.

Ninjahari said: (Jul 15, 2019)  
n(n+1)/2 is applicable. Am I right?

Bhartari Shinde said: (Jul 20, 2019)  
n(n+1)/2 = 45(45+1)/2 = 2070/2 = 1035.

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