Question

How many multiples of $6$ are between $100$ and $500$?

Answer 1

67

Explanation:

First number between 100 to 500 which is divisible by 6 is 102

Multiples of 6 between 100 to 500 :

102,102+6,102+6+6,....

This Forms an AP

a= first term = 102

d = common difference = 6

Last number between 100 to 500 which is divisible by 6 is 498

So,
`a_n=498`

Formula of nth term =
`a_n=a+(n-1)d`

`498=102+(n-1)6`

`498-102=(n-1)6`

`396=(n-1)6`

`(396)/(6)=n-1`

`66=n-1`

`66+1=n`

`67=n`

Hence there are 67 multiples of 6 between 100 to 500.