How many two-digits numbers are divisible by 3?

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Monjur Alahi

asked Feb 05, 2023

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Salim Ahmed Kawsar · Answer 1 · Feb 05, 2023 15:29:48

Salim Ahmed Kawsar

Answered Feb 05, 2023

Call

largest two digit no. divisible by 3 = 99 .

Smallest two digit no. divisible by 3 = 12 .

Now,

a₁ = 12

a_{2 = 15}

And

d = (15 - 12) ⇒ 3

Let a_n = 99

We know that by AP ,

a_n = a +[ (n-1)d ]

99 = 12 + [ (n-1)3]

99 = 12+ [ 3n - 3 ]

99 = 12 + 3n - 3

99 = 9 + 3n

3n = 99 - 9 = 90

n = 90 / 3

n = 30

Therefore , there are 30 two digits number that are divisible by 3 .

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