Question

The sum of the first $20$ terms common between the series $3+7+11+15+...$ and $1+6+11+16+...$ is

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

Answer 1

Answer: (D)

$S_1\equiv 3,7,11,15,....\Rightarrow c\cdot d=4\Rightarrow d_1=4$
$S_2\equiv 1,6,11,16,....\Rightarrow c\cdot d=5\Rightarrow d_2=5$
$\Rightarrow$ Terms common to both $A.P.$ will have $a=11$ and $d=20$
Hence, $S_{20}=\frac{20}{2}\left[\left(2\times 11\right)+\left(20-1\right)20\right]$
$=10\times 402$
$=4020$