Question
How many two-digit numbers are divisible by 3?
✓
Answer
The two digit numbers divisible by 3 are as follows:
12, 15, 18, 21, ...., 99
Clearly, this form an A.P with first term a = 12 and common difference d = 3
Last term = nth term = 99
The general term of an A.P is given by
$t_n=a+(n-1) d$
$\Rightarrow$ 99 12 + (n - 1)(3)
$\Rightarrow$ 99 = 12 + 3n - 3
$\Rightarrow$ 90 = 3n
$\Rightarrow$ n = 30
Thus 30 two-digit numbers are divisible by 3.
12, 15, 18, 21, ...., 99
Clearly, this form an A.P with first term a = 12 and common difference d = 3
Last term = nth term = 99
The general term of an A.P is given by
$t_n=a+(n-1) d$
$\Rightarrow$ 99 12 + (n - 1)(3)
$\Rightarrow$ 99 = 12 + 3n - 3
$\Rightarrow$ 90 = 3n
$\Rightarrow$ n = 30
Thus 30 two-digit numbers are divisible by 3.
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