已知Sn是等比数列{an}的前n项和,S3,S9,S6 成等差数列,求证a2,a8,a5 成等差数列.
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已知Sn是等比数列{an}的前n项和,S3,S9,S6 成等差数列,求证a2,a8,a5 成等差数列.
S3,S9,S6 成等差数列.
s3+s6=2s9
when q=1,a2,a8,a5 成等差数列.
when q不等于1;
左=a1(1-q^3)/(1-q)+a1(1-q^6)/(1-q)=2a1(1-q^9)/(1-q)
约分得:a1q^3+a1q^6=2a1q^9
两边各约去q^2;
a1q+a1q^4=2a1q^7
即a2+a5=2a8;
所以命题成立
s3+s6=2s9
when q=1,a2,a8,a5 成等差数列.
when q不等于1;
左=a1(1-q^3)/(1-q)+a1(1-q^6)/(1-q)=2a1(1-q^9)/(1-q)
约分得:a1q^3+a1q^6=2a1q^9
两边各约去q^2;
a1q+a1q^4=2a1q^7
即a2+a5=2a8;
所以命题成立
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