How to show only next line after the matched one?

If you want to stick to grep:

grep -A1 'blah' logfile | grep -v "blah"

or alternatively with sed:

sed -n '/blah/{n;p;}' logfile

you can try with awk:

awk '/blah/{getline; print}' logfile

Piping is your friend...

Use grep -A1 to show the next line after a match, then pipe the result to tail and only grab 1 line,

cat logs/info.log | grep "term" -A1 | tail -n 1

Great answer from raim, was very useful for me. It is trivial to extend this to print e.g. line 7 after the pattern

awk -v lines=7 '/blah/ {for(i=lines;i;--i)getline; print $0 }' logfile