Question

How many numbers lie between square of 12 and 13

Answer 1

Answer:

12^2 = 144 & 13^2 = 169

∴ 25 numbers lie in between.

Step-by-step explanation:

Answer 2

There are 24 numbers lie between square of 12 and 13

Given :

The square of 12 and 13

To find :

The number of numbers lie between square of 12 and 13

Concept :

The nth term of an AP is

aₙ = a + (n - 1 )d.

a = first term

aₙ = nth term

d = common difference.

Solution :

Step 1 of 3 :

Write down the given numbers

Here the given numbers are 12² and 13²

12² = 144

13² = 169

The numbers lie between square of numbers 12 and 13 are 145 , 146 , 147 , ... , 168

This is an arithmetic progression

Step 2 of 3 :

Write down first term and common difference

First term = a = 145

Common Difference = d = 146 - 145 = 1

Step 3 of 3 :

Find the number of terms

Let 168 is the nth term of the AP

⇒ a + (n - 1)d = 168

⇒ 145 + (n - 1) = 168

⇒ n + 144 = 168

⇒ n = 168 - 144

⇒ n = 24

Hence there are 24 numbers lie between square of numbers 12 and 13

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