Question

The ${10}^{\text{th}}$ term common between the series $3+7+11+15+...$ and $1+6+11+16+...$ is

Answer 1

Series are $3+7+11+15+...$ and $1+6+11+16+...$
Clearly, the first term common between the series is $11.$

Common difference of first series $=4$
Common difference of second series $=5$
$\therefore$ Common difference of series made by common terms between both series
$=L.C.M.(4,5)=20$

Now, consider an AP in which $a=11,d=20$
Required ${10}^{\text{th}}$ common term is,
$T_{10}=a+9d=11+9\left(20\right)=191$