Question

How many whole numbers each divisible by 7 lies between 200 and 700 ?

Answer 1

There are total 71 numbers between 200 and 700 which are divisible by 7.

Given:

• Numbers between 200 and 700.

To find:

• How many whole numbers each divisible by 7 lies between 200 and 700 ?

Solution:

Concept/ formula to be used:

General term of an A.P.:$\bf a_n = a + (n - 1)d$ here, 'a':first term, 'd':common difference

Step 1:

Write few terms of starting and one term from end.

After 200,

203 is the first number, which is divisible by 7.

and next number will be find after addition of 7.

So,

An AP will be formed 203,210,217,...,693

Step 2:

Find total numbers.

Write first term, common difference and last term from the AP.

$a = 203$

$d = 7$

$a_n = 693$

So,

$693 = 203 + (n - 1)7$

or

$693 - 203 = 7(n - 1)$

or

$490 = 7(n -1 )$

or

$n - 1 = \frac{490}{7}$

or

$n - 1 = 70$

or

$\bf n = 71$

Thus,

There are total 71 numbers between 200 and 700 which are divisible by 7.

Note: Do not included 700, as question asked the numbers between 200 and 700.

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Answer 2

Concept Introduction:

In mathematics, the numbers without fractions and a collection of positive integers and zero are known as whole numbers.

Given:

We have been given a range between 200 and 700.

To Find:

We have to find that how many whole numbers are present in between 200 and 700 each divisible by 7 ?

Solution:

General term of an A.P. : $a_{n}=a+(n-1) d$ here, 'a': first term, 'd': common difference.

Step 1:

After 200,

203 is the first number, which is divisible by 7 and next number will be find after addition of 7.

So,

AP series will be formed as 203,210,217,...,693

Step 2:

Writing the first term, common difference and last term from the AP series.

$a=203\\d=7\\a_{n}=693$

So,

$693=203+(n-1)7\\693-203=7(n-1)\\n-1=\frac{490}{7}\\n-1=70\\n=71$

Final Answer:

There are 71 whole numbers between 200 and 700 which are divisible by 7.

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