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, $S_{20}=\frac{20}{2}\left[\left(2 \times 11\right) + \left(20 - 1\right) 20\right]$
$= \, 10 \times 402$
$= \, 4020$