I have just started taking flying lessons and have around 10 hours. Today I was on a flight with my instructor practicing stalls and spiral dives. While the lesson itself went very well, on the way back from the practice area, while we were entering the control zone of the airport the tower warned us about traffic in front that we were to follow. While we were concentrating on following the plane in front of us, I glanced to the left and saw another traffic probably no more than 50 - 100 m away from us at the same altitude (it was hard to judge distance, but he was close enough to cover up a large portion of my window). He saw us at the same time and we did a hard right as he did a left turn to avoid us. The tower had never warned us about him, and I suspect the controller was busy with other traffic, since it was a extremely busy day today.
Does anyone have any good tips on how to scan for traffic? I find that I do have trouble spotting traffic even after ATC has called them out. Also, has anyone had experience with PCAS systems like this one and would it be worth it to get one of those so that I would at least get some warning before other airplanes get too close to me?