Answer :

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.

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