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Q.
The $10^{th}$ common term between the series $3 + 7 + 11 + ...$ and $1 + 6 + 11 + ... $is
Sequences and Series
Solution:
The first common term is $11$.
Now, the next common term is obtained by adding $ L.C.M$. of the common difference $4$ and $5$, i.e., $20$.
Therefore, $10^{th}$ common term $= T_{10}$ of the $A.P$.
whose $a = 11 $ and $d = 20$
$ \therefore T_{10} = a + 9d $
$= 11 + 9\left(20\right)$
$ = 191 $