Question

How many natural numbers lie between 8² and 9²
(a)16
(b)17
(c)18
(d)19​

Answer 1

8²=64

9²=81

16 is the answer

Answer 2

The number of natural numbers lie between 8² and 9² is 16

Given :

The numbers 8² and 9²

To find :

The number of natural numbers lie between 8² and 9² is

(a) 16

(b) 17

(c) 18

(d) 19

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 8² and 9²

8² = 64

9² = 81

The natural numbers lie between 8² and 9² are 65 , 66 , 67 , ... , 80

This is an arithmetic progression

Step 2 of 2 :

Find the number of term

The numbers are 65 , 66 , 67 , ... , 80

First term = a = 65

Common Difference = d = 66 - 65 = 1

Let 80 is the nth term of the AP

⇒ a + ( n - 1 )d = 80

⇒ 65 + ( n - 1 ) = 80

⇒ n + 64 = 80

⇒ n = 80 - 64

⇒ n = 16

The number of natural numbers lie between 8² and 9² is 16

Hence the correct option is (a) 16

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