Using $f variables with the command sed

Hello, I am familiarizing with the concept of variable, and I don't understand how to integrate one of them in a command.

In this specific case, I am searching to extract lines from a file.
The basic command to extract the 7th line is working fine.

Quote:

sed '7!d' file

Therefore, I have made a loop to extract every seventh lines of a document (for n occurrences).

Quote:

for sample in {1..n}; do echo $sample; line=$((sample*7)); sed '$line!d' file ; done

I got an error message:

Quote:

sed: -e expression #1, char 3: extra characters after command

And I do not find the answer to my problem consulting webpages, or I just do not understand the answers.

Would you have an idea why the sed command is not working with the '$line!d' variable?

Thanks for the help!