Question

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

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

Answer 1

The correct option is A $4020$

3, 7, 11, 15, 19, 23, 27, 31........... difference $=$ 4
1, 6, 11, 16, 21, 26, 31........ difference $=$ 5

common terms are 11,31....
$1^{st}$ common term, a$=$ 11

Common difference, d=20

$S_n=\frac{n}{2}(2a+(n-1\left)d\right)$

so for sum of first 20 terms

$S_{20}=\frac{20}{2}(2\times 11+(19\times 20)$

$=10\times (22+380)$

$=10\times 402$

$=4020$