Question

How many numbers lie between the squares of the following numbers? 999 and 1000​

Answer 1

zero 0

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Answer 2

The number of numbers lie between 999² and 1000² is 1998

Given :

The number 999² and 1000²

To find :

The number of numbers lie between 999² and 1000²

Concept :

If in an arithmetic progression

First term = a

Common difference = d

Then nth term of the AP

= a + ( n - 1 )d

Solution :

Step 1 of 2 :

Here the given numbers are 999² and 1000²

999² = 998001

1000² = 1000000

The natural numbers lie between 999² and 1000² are 998002 , 998003 , 998004 , ... , 999999

This is an arithmetic progression

Step 2 of 2 :

Find the number of term

The numbers are 998002 , 998003 , 998004 , ... , 999999

First term = a = 998002

Common Difference = d = 998003 - 998002 = 1

Let 999999 is the nth term of the AP

⇒ a + ( n - 1 )d = 999999

⇒ 998002 + ( n - 1 ) = 999999

⇒ n + 998001 = 999999

⇒ n = 999999 - 998001

⇒ n = 1998

Hence the number of numbers lie between 999² and 1000² is 1998

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