Question

A boy starts adding consecutive natural numbers starting from 1. After some time he reaches a total of 1000 when he realises that he has double counted a number. Find the number double counted.

Answer 1

HEY
HERE IS YOUR ANSWER
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THE NO. HE COUNTED TWICE IS 10
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HOPE IT HELPS
PLZ MARK IT AS BRAINLIEST

Answer 2

Answer:

The required number double counted is 10.

Step-by-step explanation:

Given : A boy starts adding consecutive natural numbers starting from 1. After some time he reaches a total of 1000 when he realizes that he has double counted a number.

To find : The number double counted?

Solution :

Sum of n natural numbers with a specific number x added twice is given by, $S=\frac{n(n+1)}{2}+x$

To find the value of n follow the steps :

Step 1 - Multiply the sum by 2,

$1000\times 2=2000$

Step 2 - Take the square root of the product,

$\sqrt{2000}=44.7$

Taking approximately n=44.

Now, Substitute the value of n and S in the formula

$1000=\frac{44(44+1)}{2}+x$

$1000=\frac{44(45)}{2}+x$

$1000=\frac{1980}{2}+x$

$1000=990+x$

$1000-990=x$

$x=10$

Therefore, The required number double counted is 10.