Question

How many numbers lie between square of 99 and 100

Answer 1

There are 198 numbers lie between square of 99 and 100

Given :

The square of numbers 99 and 100

To find :

The number of numbers lie between square of 99 and 100

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 3 :

Write down the given numbers

Here the given numbers are 99² and 100²

99² = 9801

100² = 10000

The numbers lie between square of 99 and 100 are 9802 , 9803 , 9804 , ... , 9999

This is an arithmetic progression

Step 2 of 3 :

Write down first term and common difference

First term = a = 9802

Common Difference = d = 9803 - 9802 = 1

Step 3 of 3 :

Find the number of terms

Let 9999 is the nth term of the AP

⇒ a + (n - 1)d = 9999

⇒ 9802 + (n - 1) = 9999

⇒ n + 9801 = 9999

⇒ n = 9999 - 9801

⇒ n = 198

Hence there are 198 numbers lie between square of 99 and 100

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