试题与答案

已知Sn为等差数列{an}的前n项和,若S3=9,S6=36,则S9的值为___

题型:填空题

题目:

已知Sn为等差数列{an}的前n项和,若S3=9,S6=36,则S9的值为______.

答案:

由等差数列的性质可得S3,S6-S3,S9-S6成等差数列,

故2(S6-S3)=S3+(S9-S6),

代入数据可得2(36-9)=9+(S9-36),

解之可得S9=81.

故答案为:81.

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