Question

how many numbers lie between the squares of 14 and 15

Answer 1

n^2 and (n+1)^2
(14)^2 and (14+1)^2

no. lie between squares is 2n
then,

2 × 14 =28

28 no. lie between squares of 14 and 15.

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Answer 2

There are 28 numbers lie between squares of 14 and 15

Given :

The square of numbers 14 and 15

To find :

The number of numbers lie between square of numbers 14 and 15

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 14² and 15²

14² = 196

15² = 225

The numbers lie between square of numbers 14 and 15 are 197 , 198 , 199 , ... , 224

This is an arithmetic progression

Step 2 of 3 :

Write down first term and common difference

First term = a = 197

Common Difference = d = 198 - 197 = 1

Step 3 of 3 :

Find the number of terms

Let 3135 is the nth term of the AP

⇒ a + (n - 1)d = 224

⇒ 197 + (n - 1) = 224

⇒ n + 196 = 224

⇒ n = 224 - 196

⇒ n = 28

Hence there are 28 numbers lie between square of numbers 14 and 15

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