Question

How many natural numbers lie between 15² and 16².​

Answer 1

Answer:

15² is 225 and 16² is 256

Hence 256-225= 31

31 -1 because we should not include 256

hence 30 natural numbers lies between 15² and 16²

Step-by-step explanation:

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Answer 2

The number of natural numbers lie between 15² and 16² is 30

Given :

The numbers 15² and 16²

To find :

The number of natural numbers lie between 15² and 16²

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 15² and 16²

15² = 225

16² = 256

The natural numbers lie between 15² and 16² are 226 , 227 , 228 , . . . , 255

This is an arithmetic progression

Step 2 of 2 :

Find the number of term

The numbers are 226 , 227 , 228 , . . . , 255

First term = a = 226

Common Difference = d = 227 - 226 = 1

Let 255 is the nth term of the AP

⇒ a + ( n - 1 )d = 255

⇒ 226 + ( n - 1 ) = 255

⇒ n + 225 = 255

⇒ n = 255 - 225

⇒ n = 30

Hence the number of natural numbers lie between 15² and 16² is 30

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