Ankush was given a problem of adding a certain number of consecutive natural numbers starting from 1, by mistake he missed a number and a sum of 800 was obtained. Find the number he missed.
A
15
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B
20
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C
25
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D
10
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Solution
The correct option is D20
We know that the sum of n natural numbers is n(n−1)2;
It is given that Ankush have missed a number, so, let the missing number be x where (x≤n) and if he obtained a sum a sum of 800 then,
n(n−1)2=800+x⇒n(n−1)=2(800+x)⇒n(n−1)=1600+2x
It shows that (n−1)2 is approximate to 1600 which implies that:
(n−1)2=1600⇒n−1=√1600⇒n−1=40⇒n=40+1⇒n=41
Now, put n=41 in the equation n(n−1)=1600+2x as shown below: