# 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

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.

 Prasannakumar said: (Nov 16, 2019) If the difference between the same throughout the series at that time only we use: 1) Sum of 'N' natural numbers(Sn) = n(n+1)/2. (Or) 2) Sn = n/2 [2a+(n-1)d] Here, d = difference. n = Total numbers. a = 1st number. Actually AP series is a,a+d,a+2d,a+3d+....+a+(n-1)d. That's why we take a=1. If we take 'x' in place of 'a' in above series, the formula will Become, Sn = n/2 [2x+(n-1)d].