This year many members of our family died with little time intervals between each one's death. I heard that we should sacrifice. Is that true? My mother dreamt that she saw her mother (who is already dead) slaughtering a chicken and some drops of its blood came on my mom's cloths?

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

Death and life are in the Hand of Allah, The Almighty. Every living being has a definite deadline which they do not exceed. Allah Says (what means): {…when their term comes, neither can they delay it nor can they advance it an hour (or a moment)."} [Quran 7:34]

On the other hand, saying that the people who lost some relatives consecutively in a short period of time, should slaughter is not backed by any evidence. As for dreams, they cannot be considered facts on which rulings should be made. The Sunnah in the situation you described is to do what Allah guided us to do. Allah Says (what means): {Who, when disaster strikes them, say, "Indeed we belong to Allah, and indeed to Him we will return." Those are the ones upon whom are blessings from their Lord and mercy. And it is those who are the [rightly] guided.} [Quran 2:156-157]

Allah knows best.