In which 1987 serial did the Seventh Doctor first appear?

The Seventh Doctor first appeared in the 1987 Doctor Who serial Time and the Rani.

The story opens with the TARDIS under attack by the renegade Time Lady known as the Rani. The damaged ship crashes on Lakertya, and the Sixth Doctor regenerates into the Seventh Doctor, played by Sylvester McCoy. His first full adventure was broadcast in four parts from 7 to 28 September 1987.

Time and the Rani is the opening serial of Doctor Who’s 24th season. The Rani has gathered brilliant minds from across time and space to power a device capable of manipulating time. The newly regenerated Doctor is confused and temporarily manipulated into helping her scheme before recovering his senses.

A common mix-up is Paradise Towers, which follows Time and the Rani as the next serial of the season. Dragonfire and Delta and the Bannermen are also Seventh Doctor stories from 1987, but neither introduces him. The story is also notable for marking McCoy’s debut in the role, even though the regeneration scene includes the Sixth Doctor only briefly.