Mathematics - Sequence & Series Question with Solution | TestHub

Given,

$3,6,9,\cdots$ upto $78$ terms

$\Rightarrow t_{78}=3+77\times 3=234$

$5,9,13,\cdots$ upto $59$ terms

$\Rightarrow t_{59}=5+58\times 4=237$

Common difference of common terms $=\mathrm{LCM}\left\{3,4\right\}=12$

First common term is $9$ and last common term is $225$

So series will be $9,21,33,\cdots ,225$  $\Rightarrow n=19$

$S=\frac{n}{2}\left[a+l\right]=\frac{19}{2}\left[9+225\right]=2223$