And when they had sung a hymn, they went out unto the mount of Olives. Some suppose that this was one particular hymn out of the Jewish service-books appointed for use at the close of the Paschal supper.
The word in the Greek is simply ὑμνήσαντες. What they sang was more probably the Hallel, consisting of six psalms, from Psalms 108:1-13, to Psalms 118:1-29, inclusive. They went out unto the Mount of Olives.
It was our Lord's custom, in these last days of his earthly life, to go daily to Jerusalem, and teach in the temple, and in the evening to return to Bethany and sup; and then after supper to retire to the Mount of Olives, and there to spend the night in prayer (Luke 21:37).
But on this occasion he did not return to Bethany. He had supped in Jerusalem. Besides, he knew that his hour was come. So he voluntarily put himself into the way of the traitor (John 18:2).