Question

How many 3 digit numbers are divisible by 7 ?​

Answer 1

14 ,21 and 28 are number divisible by 7

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Answer 2

We know,

• The first 3-digit number which is divisible by 7 is 105

• The last 3-digit number which is divisible by 7 is 994

The set of 3-digit numbers divisible by 7 = 105, 112, 119,…..994

It forms an A.P.

$\boxed{\displaystyle\sf{T(n) = a + (n - 1)d}}$

Where ,

• a = 105

• d = 7

• T(n) = 994

Applying the values to the equation,

⇒ 994 = 105 + (n – 1)7

⇒ 889 = 7n – 7

⇒ 7n = 896

⇒ n = 128

$\boxed{\displaystyle\sf{Number\:of\:three\:digit\:numbers=128}}$