The least three digit number is 100.
∴ The least 3 digit number divisible by 7 is 100 + (7 – 2) = 105
The greatest 3 digit number is 999
∴ The greatest 3 digit number divisible by 7 is 999 – 5 = 994.
∴ 3 digit numbers divisible by 7 are 105, 112, 119,….., 994.
a1 = a = 105; d = 7; a = 994
a2 = a + (n – 1)d
⇒ 994 = 105 + (n – 1)7
⇒ (n – 1)7 = 994 – 105
⇒ (n – 1)7 = 889
⇒ n – 1 = 888/9 = 127
∴ n = 127 + 1 = 128
∴ There are 128, 3 digit numbers which are divisible by 7.
(or)
\(\frac{last\,number - first \,number}{7}
\)
\(\frac{999-100}{7}\)
≃ 128.4 = 128 numbers divisible by 7.
