Ankush was given a problem of adding a certain number of consecutive natural number starting form $1$ . By mistake he missed a number and a sum of $800$ was obtained. Find the number he missed .

15

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20

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25

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10

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Solution

The correct option is D $20$
Sum of $n$ natural numbers is $\frac{n (n - 1)}{2}$
Let missing number is $x (x <= n)$ then,
$\frac{n (n - 1)}{2}$ $=$ $800 + x$
$n (n - 1)$ $=$ $1600 + 2 x$
It shows that $(n - 1)^{2}$ is approximate to $1600$ .
So, $n = 41$
Put $n = 41$
Therefore, $\frac{41 (41 - 1)}{2}$ = $800 + x$
$\Rightarrow 1640 = 1600 + 2 x$
$\Rightarrow 2 x = 40$
$\Rightarrow x = 20$

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Ankush was given a problem of adding a certain number of consecutive natural number starting form 1. By mistake he missed a number and a sum of 800 was obtained. Find the number he missed .

The correct option is D 20Sum of n natural numbers is n(n−1)2Let missing number is x(x<=n) then, n(n−1)2 = 800+x n(n−1) = 1600+2xIt shows that (n−1)2 is approximate to 1600.So, n=41Put n=41Therefore, 41(41−1)2= 800+x ⇒1640=1600+2x ⇒2x=40 ⇒x=20

Ankush was given a problem of adding a certain number of consecutive natural number starting form $1$ . By mistake he missed a number and a sum of $800$ was obtained. Find the number he missed .