(2014•安徽模拟)已知等比数列{an}的前n项和为Sn,若Sm+3-Sm+2=8(Sm-Sm-1)(m>1,m∈N)
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(2014•安徽模拟)已知等比数列{an}的前n项和为Sn,若Sm+3-Sm+2=8(Sm-Sm-1)(m>1,m∈N),且a6+4a1=S22,则a1=( )
A.
A.
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![(2014•安徽模拟)已知等比数列{an}的前n项和为Sn,若Sm+3-Sm+2=8(Sm-Sm-1)(m>1,m∈N)](/uploads/image/z/6719034-66-4.jpg?t=%EF%BC%882014%E2%80%A2%E5%AE%89%E5%BE%BD%E6%A8%A1%E6%8B%9F%EF%BC%89%E5%B7%B2%E7%9F%A5%E7%AD%89%E6%AF%94%E6%95%B0%E5%88%97%7Ban%7D%E7%9A%84%E5%89%8Dn%E9%A1%B9%E5%92%8C%E4%B8%BASn%EF%BC%8C%E8%8B%A5Sm%2B3-Sm%2B2%3D8%EF%BC%88Sm-Sm-1%EF%BC%89%EF%BC%88m%EF%BC%9E1%EF%BC%8Cm%E2%88%88N%EF%BC%89)
∵Sm+3-Sm+2=8(Sm-Sm-1)(m>1,m∈N),∴am+3=8am.∴q3=8,解得q=2.
∵a6+4a1=S22,∴a1×25+4a1=(a1+2a1)2,解得a1=4.
故选:C.
∵a6+4a1=S22,∴a1×25+4a1=(a1+2a1)2,解得a1=4.
故选:C.
(2014•安徽模拟)已知等比数列{an}的前n项和为Sn,若Sm+3-Sm+2=8(Sm-Sm-1)(m>1,m∈N)
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