How many three digit numbers are divisible by 7?

Smallest 3-digit number that is divisible by 7 is 105 and greatest 3-digit number that is divisible by 7 is 994.
Let the no. of three digits numbers that are divisible by 7 be n.

Thus, a_n = 994, first term a = 105 and common difference d = 7.

Since, a_n = a + (n - 1)d

Where,

a = First term of AP
d = Common difference of AP
and no of terms is ‘n’

⇒ 994 = 105 + (n - 1) × 7
⇒ 994 – 105 = 7 × (n - 1)
⇒ 889 = 7 × (n - 1)
⇒ 127 = n – 1
⇒ n = 128

Hence, Total 3-digit numbers that are divisible by 7 are 128.