find the number of natural numbers between 200 and 700 which are multiples of 11

The numbers between 200 and 700 which are multiples of 11:

209, 220, ......, 693

 

This is an AP with first term = a = 209 and common difference = d = 11.

 

Let the number of terms be n.

a_n = a + (n - 1)d

₆₉₃ = 209 + (n - 1)(11)

(n - 1)(11) = 484

n - 1 = 44

n = 45

 

Thus, there are 45 natural numbers between 200 and 700 which are multiples of 11.