Question

how many natural numbers lie between 19 square and 20 square​

Answer 1

SOLUTION

TO DETERMINE

The number of natural numbers lie between 19 square and 20 square

CONCEPT TO BE IMPLEMENTED

If in an arithmetic progression

First term = a

Common difference = d

Then nth term of the AP

= a + ( n - 1 )d

EVALUATION

Here the given numbers are 19² and 20²

19² = 361

20² = 400

The natural numbers lie between 19 square and 20 square are 362 , 363 , 364 , . . . , 399

This is an arithmetic progression

First term = a = 362

Common Difference = d = 363 - 362 = 1

Let 399 is the nth term of the AP

⇒ a + ( n - 1 )d = 399

⇒ 362 + ( n - 1 ) = 399

⇒ n + 361 = 399

⇒ n = 399 - 361

⇒ n = 38

FINAL ANSWER

The number of natural numbers lie between 19 square and 20 square = 38

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