I had a show at 38 weeks and then went 8 days over.
I had an OB appt the day I had Caleb and he did a stretch & sweep which could have got things moving.
He wasn't interested in admitting and inducing me untill I was at least 10 days over.
You don't have to be induced if you've had the show, it's just a sign that your cervix is softening and opening up.