Question

How many numbers between 1-100 are equal to five times an odd number?​

Answer 1

There are 10 numbers between 1-100 which are equal to 5 times an odd number.

Step-by-step explanation:

The odd numbers between 1 and 100 are 1,3,5,7…..

When these when these odd numbers are multiplied by 5 we get the following result.

`5 * 1=5`

`5 * 3=15`

`5 * 19=95`

These products form an AP 5,15,25,…..,95

common difference d=10

first term
`a=5`

last term
`a_n=95`

we have to calculate the number of terms n

The expression for last term
`a_n` of an AP is

`a_n=a+(n-1)d`

`a_n=a+nd-d`

`nd=a_n-a+d =95-5+10=100`

`n= (100)/(d)= (100)/(10)=10`