Tzom Gedaliah

On Rosh Hashana, the first two days of Aseres Yemei Teshuva, we all daven for life; but on the third day - the day Gedaliah was murdered, which caused the downfall for Klal Yisroel - we need to daven for a double dose of Heavenly mercy. We ask that we be uplifted from the downfall of Gedaliah's murder, and inscribed for a year of life.

(Maharsha)