Mathematics - Sequence & Series Question with Solution | TestHub

Given,

Two A.P's  as

$3,7,11,15,...$ 

First term$\left(a_1\right)=3$

Common difference$\left(d_1\right)=4$

And,

$1,6,11,16,...$,

First term$\left(a_2\right)=1$

Common difference $\left(d_2\right)=5$

Now, common difference of the series of the common terms of the given A.P's is $d=\mathrm{LCM}\left(d_1,d_2\right)=\mathrm{LCM}\left(4,5\right)=20$

Now, series of common term is 

$11,31,51,71,...$

So, $8^{\mathrm{th}}$ common term appearing in the both the series is

$a_8=11+\left(8-1\right)d$

$\Rightarrow a_8=11+7\times 20=151$