"And the life of Sarah." Why did it say "and the life of Sarah"? Rather it is to teach that she did not truly live until Isaac was born. From where do we know this?
From the numerical value of "and they were (vayihyu=37, Isaac's age when Sarah died)". From here we learn that anyone who does not have children does not have life. Not only that, rather that person is considered like one who is dead, as it is stated, "give me children." (Genesis 30:1) Another interpretation: "And the life of Sarah." When she was 100, she was like 20 in sin, and when she was 20 she was like a 7 year old in beauty.
Therefore, they said 100 and 20 and 7 years. Another interpretation: "And the life of Sarah." Why is this parsha next to the verse above, as it is stated: "Milcah has borne?" This is what that sage said: "The sun rises and the sun sets." (Ecclesiastes 1:5) That the sun of Rebecca rose before the death of Sarah, our mother.
Another interpretation: "And the life of Sarah etc." Therefore they counted out Sarah's years of life to tell you that it was due to the merit of Sarah who lived 127 years, that Esther would rule over 127 provinces. Another interpretation: "And the life of Sarah." Why is Sarah's death placed after the binding of Isaac? To tell you that when Abraham came from Mount Moriah, he found Sarah had died because of the words of the Satan.
Therefore they blow the Shofar on Rosh Hashanah in order that Sarah's death can serve as atonement for them, since the shofar blast is a cry and a wail.