Question

how many numbers are divisible by 9 between 1 and 300?

Answer 1

33 numbers are between 1 and 300, which are divisible by 9.

Given:

• Numbers between 1 and 300.

To find:

• How many number are divisible by 9.

Solution:

Concept to be used:

• It will form an A.P., if 'a' is the first term and 'd' is common difference, then number of terms can be find by the formula of general term.
• $\bf a_n = a + (n - 1)d$

Step 1:

Write some numbers which are divisible by 9.

We know that

9, 18, 27,..., 297

are the number between 1 to 300 which are divisible by 9.

Step 2:

Find total numbers.

As

First term of AP is 'a'=9

Common difference 'd'= 9

Last term $\bf a_n = 297$

Put these values in formula of general term and find number of terms in the A.P.

$297 = 9 + (n - 1)9$

or

$297 - 9 = (n - 1)9$

or

$288 = 9(n - 1)$

or

$n - 1 = \frac{288}{9}$

or

$n - 1 = 32$

or

$\bf n = 33$

Thus,

Total 33 numbers are between 1 and 300, which are divisible by 9.

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