Question

how many numbers lie between the squares of 78 and 79

Answer 1

There are 156 numbers lie between squares of 78 and 79

Given :

The square of numbers 78 and 79

To find :

The number of numbers lie between the squares of 78 and 79

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 3 :

Write down the given numbers

Here the given numbers are 78² and 79²

78² = 6084

79² = 6241

The numbers lie between squares of 78 and 79 are 6085 , 6086 , 6087 , ... , 6240

This is an arithmetic progression

Step 2 of 3 :

Write down first term and common difference

First term = a = 6085

Common Difference = d = 6086 - 6085 = 1

Step 3 of 3 :

Find the number of terms

Let 6240 is the nth term of the AP

⇒ a + (n - 1)d = 6240

⇒ 6085 + (n - 1) = 6240

⇒ n + 6084 = 6240

⇒ n = 6240 - 6084

⇒ n = 156

Hence there are 156 numbers lie between squares of 78 and 79

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Answer 2

Given: 78 and 79

Square of 78 and 79 is,

$78^2=6084\\79^2=6241$

Numbers between the square of 78 and 79 are,

6085, 6086, 6087,..........., 6240.

$6240-6085+1=155+1\\=156$

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