The least three digit number is 100.

∴ The least 3 digit number divisible by 7 is 100 + ( – ) =

The greatest 3 digit number is

∴ The greatest 3 digit number divisible by 7 is 999 – = .

∴ 3 digit numbers divisible by 7 are

105, 112, 119,….., 994.

a₁ = a = ; d = ; a_n =

a_n = a + (n – 1)d

⇒ = + (n – 1)

⇒ (n – 1) = –

⇒ (n – 1) =

∴ n = + =

∴ There are , 3 digit numbers which are divisible by 7.

Note: If the common difference for any two A.Ps are equal then difference between n^th terms of two A.Ps is same for all natural values of n.