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
$\Rightarrow 11+20 \times 9$
$\Rightarrow 191$
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