Can a State Trooper pull you over for a speeding ticket if your behind them?

One day it had rained and I had came from my cousin house the back way and I was coming down this little hill and there was a car was in front of me. It was night time and it had pressed on brakes and pulled to the side. So I slowed down cause I thought he was going to turn but he pulled over. As soon as i past him to go around this curve. I found out it was a State Trooper and he pulled me over. He told me that he clocked me coming down the hill going 70 or 71mph but i was going 60mph but what got me was that he said that i slowed down because i know it was him in front of me. But that was impossible because it was a country road with very little light and i didn't get close to him until he pressed brakes i think he pulled me because it was Christmas Day.