Question

How many numbers of two digit are divisible by 3?

Answer 1

Hint: Convert the problem in the form of an AP and use the nth term of an AP formula to determine the number of terms in that sequence.

Complete step-by-step answer:

The two digit numbers which are divisible by 3 are-
$\Rightarrow$ 12, 15, 18, 21,..................., 99
So, this sequence forms an A.P.

First term of the A.P. = $a_1$ = 12
Common difference of the A.P. = d = 15 - 12 = 3
Last term of the A.P. = 99

nth term of an A.P. is given by

$a_n=a_1+\left(n-1\right)d$

Substituting the values in the above formula,

$\Rightarrow 99=12+\left(n-1\right)3$
$\Rightarrow \left(n-1\right)={\displaystyle \frac{99-12}{3}}=29$
$\Rightarrow n=29+1=30$
Hence there are 30, two digit numbers which are divisible by 3.

Note: These types of problems can be solved using converting the problem statement in the form of a sequence and then use the formulas in that respective sequence to determine the necessary quantities.