Class 11

Math

Algebra

Sequences and Series

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

- $4020$
- $4220$
- $4200$
- $4000$

1, 6, 11, 16, 21, 26, 31........ difference $=$ 5

common terms are 11,31....

$1_{st}$ common term, a$=$ 11

$1_{st}$ common term, a$=$ 11

Common difference, d=20

$S_{n}=2n (2a+(n−1)d)$

so for sum of first 20 terms

$S_{20}=220 (2×11+(19×20)$

$=10×(22+380)$

$=10×402$

$=4020$