**Question:**

What is the $10^{\text {th }}$ common term between the APs $3,7,11,15,19, \ldots$ and 1,6 , 11, 16, …?

**Solution:**

To find: $10^{\text {th }}$ common term between the APs

Common difference of $1^{\text {st }}$ series $=4$

Common difference of $2^{\text {nd }}$ series $=5$

LCM of common difference will give us a common difference of new series

$\Rightarrow 5 \times 4$

$\Rightarrow 20$

The first term of new AP will be 11 , so the $10^{\text {th }}=$ term of this series is

$\Rightarrow 11+20 \times 9$

$\Rightarrow 191$