And you shall take them on the first day
Vayikra Rabba, Chapter 30, Clause 7
"And you shall take them on the first day" * - this is the fifteenth day and you say, on the first day?
Rabbi Yehoshua of Sichnin in the name of Rabbi Levi said: it is likened to a state that owed Lips (taxes) to the king and the king had arrived to collect it. Within ten miles of the state, the great men of the state went out and praised the king – consequently, he waived a third of the owed amount... Within five miles the state's middle-class representatives came out and praised the king – so he then waived another third of the amount. When he actually entered the country, the entire populace of the state, men and women and children, went out and praised him – so then he waived the entire amount.
The king said to them, "Let bygones be bygones, we shall begin a new calculation from now on". Thus, on the eve of Rosh Hashana, the greatest men of the generation fast and God waives the punishments for one-third of their sins. And from Rosh Hashana until the Day of Atonement individuals fast and G-d waives the punishments of another third of their sins. And on the Day of Atonement, all of the populace, men, women and children fast and G-d tells them: Let bygones be bygones and from now we shall commence a new calculation.
And from Yom Kippur until the holiday of Sukkot, all of Israel gets busy fulfilling commandments: One person is busy with his sukkah and another one – with his lulav. And on the first day of the festival of Sukkot all of Israel stand before G-d with their lulavs and etrogs in their hands and praise the name of G-d. And G-d tells them: "Let bygones be bygones, from now on, we shall begin to calculate sins and good deeds." Therefore, Moses warns Israel, "And you shall take them on the first day."
*According to Leviticus, 23, 39-40: 39 “‘But on the fifteenth day of the seventh month, when you gather the crops of the land, you shall celebrate the festival of G-d for seven days; the first day is a day of sabbath rest, and the eighth day also is a day of sabbath rest. 40 On the first day you are to take a fruit from beautiful trees, a frond of a palm tree, a branch of a leafy tree and brook willows—and rejoice before the G-d your Lord for seven days.