设Sn是等比数列的前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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设Sn是等比数列的前n项和,S3,S9,S6成等差数列 求证a2,a8,a5成等差数列
设Sn是等比数列的前n项和,S3,S9,S6成等差数列 求证a2,a8,a5成等差数列

设Sn是等比数列的前n项和,S3,S9,S6成等差数列 求证a2,a8,a5成等差数列
首项a
2S9=2a(q^9-1)/(q-1)
S3+S6=a(a^3-1)/(q-1)+a(a^6-1)/(q-1)
2S9=S3+S6
显然a不等于0
2(q^9-1)=a^3-1+q^6-1
2q^9=q^3+q^6
2q^7=q+q^4
2aq^7=aq+aq^4
2a8=a2+a5
所以a2,a8,a5成等差数列

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