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:
21 comments Page 1 of 3.
Keerthika said:
2 weeks ago
It's simply n(n+1)%2.
So that, 45(45+1)%2 = 1035.
So that, 45(45+1)%2 = 1035.
Kiran Kumar said:
3 weeks ago
1 + 2 + 3 ................45.
45 + 44 + 23 + .........1.
Then;
46+46+...........45 terms.
= 46 * 45/2 = 1035.
from above we get formula like n*(first+last)/2 where n is the no of numbers
45 + 44 + 23 + .........1.
Then;
46+46+...........45 terms.
= 46 * 45/2 = 1035.
from above we get formula like n*(first+last)/2 where n is the no of numbers
KrishanuS said:
1 year 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.
(1)
Nivetha said:
6 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)
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)
Bhartari Shinde said:
7 years ago
n(n+1)/2 = 45(45+1)/2 = 2070/2 = 1035.
(2)
Ninjahari said:
7 years ago
n(n+1)/2 is applicable. Am I right?
(1)
Md Ikramul Haque said:
8 years ago
4+5=9.
And 1035=1+0+3+5=9.
Answer is A.
And 1035=1+0+3+5=9.
Answer is A.
(13)
Jignesh said:
8 years ago
Good method @Rohit.
Rinkal said:
8 years ago
I like your method, thanks @Rohit.
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