Aptitude - Numbers - Discussion
Discussion Forum : Numbers - General Questions (Q.No. 20)
20.
The sum of first 45 natural numbers is:
Answer: Option
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 |
Discussion:
19 comments Page 1 of 2.
Bill said:
1 decade ago
Help me to find even more easy way.
K.pavan said:
1 decade ago
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:
1 decade ago
[N/2]*(first term + last term).
Rohit Singla said:
1 decade ago
Middle no.of 45 is 23.
So its average is also 23.
23*45 = 1035.
So its average is also 23.
23*45 = 1035.
(1)
Piyosh said:
10 years ago
Is this n(n+1)/2 applicable for all A.P?
Smiley said:
9 years ago
Does the shortcut method work in every case?
Rohan said:
9 years ago
@Rohit, I like your method quit interesting.
Vinayak said:
9 years ago
@Rohit.
I like your method it's a simple thing to get an answer.
I like your method it's a simple thing to get an answer.
BIMAL said:
9 years ago
Sum upto nth of natural numbers = n* (n + 1)/2,
Put n = 45 here.
Put n = 45 here.
Manali said:
9 years ago
Simplest way to multiply the given number with its consecutive number and then divide by 2.
i.e (45 * 46)/2 = 1035.
i.e (45 * 46)/2 = 1035.
(1)
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