The unique mitzvot of Sukkot are not observed on Shemini Atzeret. Furthermore, unlike Sukkot, when numerous offerings were sacrificed each day in the Temple, on Shemini Atzeret only one bull and one ram were offered. The Sages see this as an expression of the close ties between God and the people of Israel.

“You shall present a burnt offering…to the Lord: one bull, one ram” (Numbers 29:36). This is comparable to a king who made a feast for seven days and invited all his people for the seven days of the feast. When the seven days of the feast had passed, he said to his beloved servant: We have fulfilled our obligation to the people, let you and I suffice with whatever you find: A litra of meat or fish or vegetables. Similarly, the Holy One, blessed be He, said to Israel: All the offerings that you brought over the seven days of the festival of Sukkot, you brought them on behalf of the nations of the world, but “on the eighth day it shall be an assembly for you” (Numbers 29:36); suffice with what you find, one bull and one ram.

To what do these seventy bulls that are brought over the seven days of Sukkot correspond? They correspond to the seventy nations. Why is a single bull brought on Shemini Atzeret? It corresponds to the single nation of Israel. This can be explained by means of a parable of a flesh-and-blood king who said to his servants: Prepare for me a great feast. On the last day, he said to his beloved servant: Prepare for me a small feast so that I can enjoy your company alone. (Tanĥuma [Buber] 15; Sukka 55b)