高中等比数列设等比数列的前n项和为Sn,若Sm=A,S2m-Sm=B,S3m-S2m=C,则下列等式一定成立的是()A、
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高中等比数列
设等比数列的前n项和为Sn,若Sm=A,S2m-Sm=B,S3m-S2m=C,则下列等式一定成立的是()
A、AB=C B、AC=B² C、A+B=C D、A+C=2B
设等比数列的前n项和为Sn,若Sm=A,S2m-Sm=B,S3m-S2m=C,则下列等式一定成立的是()
A、AB=C B、AC=B² C、A+B=C D、A+C=2B
![高中等比数列设等比数列的前n项和为Sn,若Sm=A,S2m-Sm=B,S3m-S2m=C,则下列等式一定成立的是()A、](/uploads/image/z/17929601-17-1.jpg?t=%E9%AB%98%E4%B8%AD%E7%AD%89%E6%AF%94%E6%95%B0%E5%88%97%E8%AE%BE%E7%AD%89%E6%AF%94%E6%95%B0%E5%88%97%E7%9A%84%E5%89%8Dn%E9%A1%B9%E5%92%8C%E4%B8%BASn%2C%E8%8B%A5Sm%3DA%2CS2m-Sm%3DB%2CS3m-S2m%3DC%2C%E5%88%99%E4%B8%8B%E5%88%97%E7%AD%89%E5%BC%8F%E4%B8%80%E5%AE%9A%E6%88%90%E7%AB%8B%E7%9A%84%E6%98%AF%EF%BC%88%EF%BC%89A%E3%80%81)
A=Sm=a(q^m-1)/(q-1)
B=S2m-Sm=a(q^2m-1)/(q-1)-a(q^m-1)/(q-1)=a(q^2m-q^m)/(q-1)=aq^m(q^m-1)/(q-1)
C=S2m-S2m=a(q^3m-1)/(q-1)-a(q^2m-1)/(q-1)=aq^2m(q^m-1)/(q-1)
显然,AC=B^2,选B
B=S2m-Sm=a(q^2m-1)/(q-1)-a(q^m-1)/(q-1)=a(q^2m-q^m)/(q-1)=aq^m(q^m-1)/(q-1)
C=S2m-S2m=a(q^3m-1)/(q-1)-a(q^2m-1)/(q-1)=aq^2m(q^m-1)/(q-1)
显然,AC=B^2,选B
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