Question

How many natural numbers lie between 182and 192 ?
a)30
b)37
c)35
d)36​

Answer 1

Answer:

30

Step-by-step explanation:

1211

Answer 2

SOLUTION

COMPLETE QUESTION

TO CHOOSE THE CORRECT OPTION

The number of natural numbers lie between 18² and 19²

a) 30

b) 37

c) 35

d) 36

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 18² and 19²

18² = 324

19² = 361

The natural numbers lie between 18² and 19² are 325 , 326 , 327 , ... , 360

This is an arithmetic progression

First term = a = 325

Common Difference = d = 326 - 325 = 1

Let 360 is the nth term of the AP

⇒ a + ( n - 1 )d = 360

⇒ 325 + ( n - 1 ) = 360

⇒ n + 324 = 360

⇒ n = 360 - 324

⇒ n = 36

The number of natural numbers lie between 18² and 19² is 36

FINAL ANSWER

Hence the correct option is d) 36

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