Question

The sum of first $20$ common terms between the series $3+7+11+15+\cdots$ and $1+6+11+\cdots$ is

• A. $4000$
• B. $4200$
• C. $4220$
• D. $4020$

Answer 1

The correct option is D $4020$

$S_1:3,7,11,\dots$
Here, $d_1=4$
$S_2:1,6,11,\dots$
Here, $d_2=5$
$\Rightarrow$ Terms common to both A.P. will have $a=11$ and $d=L.C.M.(4,5)=20$
$\therefore S_{20}=\frac{20}{2}\left[2\right(11)+(20-1\left)20\right]=4020$