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 2 of 2.
Tohid said:
8 years ago
n(n + 1)÷2 = 45(45 + 1)÷2 = 1035.
(1)
Rinkal said:
8 years ago
I like your method, thanks @Rohit.
Jignesh said:
8 years ago
Good method @Rohit.
Md Ikramul Haque said:
7 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)
Ninjahari said:
6 years ago
n(n+1)/2 is applicable. Am I right?
(1)
Bhartari Shinde said:
6 years ago
n(n+1)/2 = 45(45+1)/2 = 2070/2 = 1035.
(1)
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)
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)
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.
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