试题与答案

已知等差数列{an}前三项的和为-3,前三项的积为8. (1) 求等差数列{an

题型:解答题

题目:

已知等差数列{an}前三项的和为-3,前三项的积为8.

(1) 求等差数列{an}的通项公式;

(2) 若数列{an}单调递增,求数列{an}的前n项和.

答案:

(1) an=-3n+5,或an=3n-7.(2)

题目分析:本题有等差数列的通项公式入手,只要解决和d两个量问题即可解决,所以需要找到两个关系,列出两个方程即可,条件中恰有前三项和与前三项积两个条件,因此可以列出两个方程.

解:(1)设等差数列{an}的公差为d,则,a3=a1+2d.

由题意得

解得

所以由等差数列通项公式可得

an=2-3(n-1)=-3n+5,或an=-4+3(n-1)=3n-7.

故an=-3n+5,或an=3n-7.

(2)由数列{an}单调递增得:an=3n-7.

数列{an}的前n项和 .

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