How many numbers between 100 and 1000 are completely divisible by 11?

To find: the numbers between 100 and 1000 that are divisible by 11.

l = a + (n – 1)d

Where, l = last term, a = first term, n = no. of terms, d = common difference

The first term (a) divisible by 11 = 110

Last term(l) divisible by 11 = 990

Now, substituting values;

990 = 110 + (n – 1) 11

990 – 110 = (n – 1)11

880 = (n – 1) 11

n – 1 = $$\frac{880}{11}$$​​

n = 80 + 1

n = 81

Thus, Total numbers between 100 to 1000 divisible by 11 is 81.