Question

How many numbers of two digit are divisible by 3?

Answer 1

In this problem, we need to find out how many two-digit numbers are divisible by 3.

So, we know that the first two-digit number that is divisible by 3 is 12, and the last two-digit number divisible by 3 is 99. Also, all the terms that are divisible by 3 will form an A.P. with a common difference of 3.

So here,

First term (a) = 12

Last term (a_n) = 99

Common difference (d) = 3

So, let us take the number of terms as n

Now, as we know,

a_n = a + (n − 1)d

So, for the last term,

99 = 12 + (n − 1)3

99 = 12 + 3n − 3

99 = 9 + 3n

99 − 9 = 3n

Further simplifying,

90 = 3n

`n = 90/3`

n = 30

Therefore, the number of two-digit terms divisible by 3  is 30