If you opt for awk, you can use its NR variable which contains the number of input records so far.
Suppose the text file is somefile:
$ cat > somefile.txt
Line 1
Line 2
Line 3
Line 4
To print a single line number, say line 2:
$ awk 'NR==2' somefile.txt
Line 2
If the text file is huge, you can cheat by exiting the program on the first match. Note that this hack will not work if multiple lines are being extracted.
$ awk 'NR==2 {print;exit}' somefile.txt
Line 2
To extract a section of the text file, say lines 2 to 3:
awk 'NR==2,NR==3' somefile.txt
Line 2
Line 3
A more interesting task is to extract every nth line from a text file. I showed previously how to do it using sed and perl.
Using awk, to print every second line counting from line 0 (first printed line is line 2):
$ awk '0 == NR % 2' somefile.txt
Line 2
Line 4
To print every second line counting from line 1 (first printed line is 1):
$ awk '0 == (NR + 1) % 2' somefile.txt
Line 1
Line 3
% is the mod (i.e. remainder) operator.