Question

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

Answer 1

Answer:

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

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.

$5 \times 1=5$

$5 \times 3=15$

$5 \times 19=95$

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  

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

$a_n=a+nd-d$

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

$n= \frac{100}{d}= \frac{100}{10}=10$