Aptitude - Numbers - Discussion
Discussion Forum : Numbers - General Questions (Q.No. 62)
62.
(51 + 52 + 53 + ... + 100) = ?
Answer: Option
Explanation:
Sn = (1 + 2 + 3 + ... + 50 + 51 + 52 + ... + 100) - (1 + 2 + 3 + ... + 50)
| = | 100 | x (1 + 100) - | 50 | x (1 + 50) |
| 2 | 2 |
= (50 x 101) - (25 x 51)
= (5050 - 1275)
= 3775.
Discussion:
18 comments Page 1 of 2.
Crista Ronaldo suiii said:
2 years ago
Question: (51 + 52 + 53 + ... + 100) = ?
Formula: n/2(Last number + First number).
n = 50,
Last number = 100,
First number = 51.
50/2(100 + 51) => 25 x 151 = 3775.
Formula: n/2(Last number + First number).
n = 50,
Last number = 100,
First number = 51.
50/2(100 + 51) => 25 x 151 = 3775.
(23)
Shivam said:
4 years ago
We can also do like this;
a=51, n=50, l=100.
Sn=n/2(a+l),
= 50/2(51+100),
= 25 x 151,
= 3775 ans.
a=51, n=50, l=100.
Sn=n/2(a+l),
= 50/2(51+100),
= 25 x 151,
= 3775 ans.
(12)
Ujjwal Thakur (Dada) said:
4 years ago
+1+2+3+.......+50+51+52+53+.......+100-(1+2+3......+50).
Note: before 1 to 50 add, to after 1 to 50 multiple,
N1= 100,
N2= 50,
Formula= n(n+1)/2.
So, 100(100+1)/2 - 50(50+1)/2.
100 * 101/2 - 50 * 51/2.
50 * 101-25 * 51= 5050 - 1275 = 3755 answer.
Note: before 1 to 50 add, to after 1 to 50 multiple,
N1= 100,
N2= 50,
Formula= n(n+1)/2.
So, 100(100+1)/2 - 50(50+1)/2.
100 * 101/2 - 50 * 51/2.
50 * 101-25 * 51= 5050 - 1275 = 3755 answer.
(6)
DR. Roshan said:
9 years ago
Very easy way guys.
Total numbers = 50.
Middle number from 51 - 100 = 75.5.
Just multiply the middle number with 50.
i.e. 75.5 * 50 = 3775.
Total numbers = 50.
Middle number from 51 - 100 = 75.5.
Just multiply the middle number with 50.
i.e. 75.5 * 50 = 3775.
(4)
Kinal said:
4 years ago
Thank you everyone for explaining.
(3)
Kishor said:
4 years ago
Thank you for explaining @Pooja.
(2)
Khemsingh gurjar jaisingh said:
7 years ago
Solved 50/2(51+100).
=25*151,
=3775 [n/2=50/2=25.
=25*151,
=3775 [n/2=50/2=25.
(2)
Ankita Thakur said:
1 decade ago
The formula for sum of series = n/2[first number + last number].
Now we have to find n= [(last number - first number) / common difference]+1.
= [(100 - 51)/1] + 1.
= 50.
Therefore as @Pooja said sum of series = 50/2[50+100].
= 151*25.
= 3775.
Now we have to find n= [(last number - first number) / common difference]+1.
= [(100 - 51)/1] + 1.
= 50.
Therefore as @Pooja said sum of series = 50/2[50+100].
= 151*25.
= 3775.
(1)
Khushi said:
1 decade ago
You guys also can do that.
a=51, n=50, d=1 so,
sn=n/2[2a+ (n-1) d].
= 50/2[2*51+(50-1)*1].
= 25[102+49].
= 25*151.
= 3775.
a=51, n=50, d=1 so,
sn=n/2[2a+ (n-1) d].
= 50/2[2*51+(50-1)*1].
= 25[102+49].
= 25*151.
= 3775.
(1)
Prithvi said:
6 years ago
Thanks all for explaining the answer.
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