Question

Find how many three digit natural numbers are divisible by 5.

Answer 1

The three digit natural numbers divisible by 5 are 100, 105, 110, …, 995.

The above sequence is an A.P.

∴ a = 100, d = 105 – 100 = 5

Let the number of terms in the A.P. be n.

Then, t_n = 995

Since, t_n = a + (n – 1)d

∴ 995 = 100 + (n – 1)5

∴ 995 – 100 = (n – 1)5

∴ 895 = (n – 1)5

∴ n – 1 = `895/5`

∴ n – 1 = 179

∴ n = 179 + 1 = 180

∴ There are 180 three digit natural numbers which are divisible by 5.