Question

The number of terms common to the A.P.'s $3,7,11,\cdots ,407$ and $2,9,16,\cdots ,709$ is

Answer 1

First common term is 23
Common difference = LCM $(7,4)=28$
$\Rightarrow 23+(n-1)28\le 407$
$\Rightarrow n-1\le 13.71$
$\Rightarrow n=14$