Question

Find the number of multiples of 7 between 30 and 300. Is it 38?

Answer 1

In the above problem, you want to find the number of multiples of 7 between 30 and 300. 

This is an Arithmetic progression where you have n number of terms between 30 and 300 that are multiples of 7. So it is evident that the common difference here is 7.

Arithmetic progression is a sequence of numbers where each new number in the sequence is generated by adding a constant value (in the above case, it is 7) to the preceding number, called the common difference (d)

In the above case, the first number after 30 that is a multiple of 7 is 35

So first number (a) = 35

The last number in the sequence less than 300 that is a multiple of 7 is 294

So, last number (l) = 294

Common difference (d) = 7

The formula to find the number of terms in the sequence (n) is,

n = ((l - a) ÷ d) + 1 = ((294 - 35) ÷ 7) + 1 = (259 ÷ 7) + 1 = 37 + 1 = 38