In a statement, his family said: "Our son Adam left home on Wednesday afternoon (9 November) to go in town, where he was seen talking and having a laugh with people he met in the Tooth and Claw pub.
"He last spoke to his father at 20:30 in the evening."
Mr Mitchell is known to have left another pub, Wetherspoons, just after 00:00 and he was alone when seen walking down the Longman at 01:00 on CCTV on 10 November, his family said.
The statement said: "Adam is a typical teenager who loves heavy metal music. He constantly wore his off-cut denim jacket that was decorated with patches of his favourite bands, it was his pride and joy.
"He was wearing it when he was last seen over the top of his leather jacket, he always wore black jeans and black boots."