Question

How many multiples of $3$ lie between $20$ and $205$?

• A. $59$
• B. $61$
• C. $62$
• D. $63$

Answer 1

Answer: (C)

$62$

Multiples of $3$ between $20$ and $205$ are:
$21,24,27,........,204$
This sequence forms an AP. with first term $a=21$ , common difference $d=24-21=3$ and last term $l=204$
Since, $l=a+(n-1)d$
$\Rightarrow 204=21+(n-1)3$
$\Rightarrow 204-21=(n-1)3$
$\Rightarrow 183=(n-1)3$
$\Rightarrow 61=n-1$
$\Rightarrow n=62$
Option C is correct.