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.
Prasannakumar said:
6 years ago
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].
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].
(2)
KrishanuS said:
10 months ago
In 45 there are odd numbers of odd numbers. 23 odd numbers so the answer of sum gonna be another odd number.
Hence 1035 is the answer (As there is only one odd number). If there is more than one apply n* (n+1) /2.
Hence 1035 is the answer (As there is only one odd number). If there is more than one apply n* (n+1) /2.
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)
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
Nivetha said:
5 years ago
The formula for an average of natural numbers is n+1/2,
45+1/2 = 23,
Therefore, 45 natural numbers *23 = 1035.
45+1/2 = 23,
Therefore, 45 natural numbers *23 = 1035.
(9)
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.
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)
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.
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