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 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 

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. 