Print lines ending with string within a range of lines

sed -n '/dmitritelinov/,${/nologin$/p;}' /etc/passwd

The range of lines being chosen are starting from the line containing the pattern dmitritelinov till the end of the file($).
The commands present within the braces are applied only for this range of lines. Within this group, only the lines ending with nologin are printed.

To print the same between the root and dmitritelinov strings:

sed -n '/root/,/dmitritelinov/{/nologin$/p;}' /etc/passwd