1.已知数列{An}满足A1=1,An= 2A(n-1)+2(n∈N,且N≥2)(1)求A1,A2(2)设bn=An+2,证明数列{bn}是等比数列,并指出其首项和公比2.已知数列{An}满足A1=-1,An+1=2An,求该数列前十项的和S10
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![1.已知数列{An}满足A1=1,An= 2A(n-1)+2(n∈N,且N≥2)(1)求A1,A2(2)设bn=An+2,证明数列{bn}是等比数列,并指出其首项和公比2.已知数列{An}满足A1=-1,An+1=2An,求该数列前十项的和S10](/uploads/image/z/2684582-62-2.jpg?t=1.%E5%B7%B2%E7%9F%A5%E6%95%B0%E5%88%97%7BAn%7D%E6%BB%A1%E8%B6%B3A1%3D1%2CAn%3D+2A%EF%BC%88n-1%EF%BC%89%2B2%EF%BC%88n%E2%88%88N%2C%E4%B8%94N%E2%89%A52%EF%BC%89%EF%BC%881%EF%BC%89%E6%B1%82A1%2CA2%282%29%E8%AE%BEbn%3DAn%2B2%2C%E8%AF%81%E6%98%8E%E6%95%B0%E5%88%97%7Bbn%7D%E6%98%AF%E7%AD%89%E6%AF%94%E6%95%B0%E5%88%97%2C%E5%B9%B6%E6%8C%87%E5%87%BA%E5%85%B6%E9%A6%96%E9%A1%B9%E5%92%8C%E5%85%AC%E6%AF%942.%E5%B7%B2%E7%9F%A5%E6%95%B0%E5%88%97%7BAn%7D%E6%BB%A1%E8%B6%B3A1%3D-1%2CAn%2B1%3D2An%2C%E6%B1%82%E8%AF%A5%E6%95%B0%E5%88%97%E5%89%8D%E5%8D%81%E9%A1%B9%E7%9A%84%E5%92%8CS10)
1.已知数列{An}满足A1=1,An= 2A(n-1)+2(n∈N,且N≥2)(1)求A1,A2(2)设bn=An+2,证明数列{bn}是等比数列,并指出其首项和公比2.已知数列{An}满足A1=-1,An+1=2An,求该数列前十项的和S10
1.已知数列{An}满足A1=1,An= 2A(n-1)+2(n∈N,且N≥2)
(1)求A1,A2
(2)设bn=An+2,证明数列{bn}是等比数列,并指出其首项和公比
2.已知数列{An}满足A1=-1,An+1=2An,求该数列前十项的和S10
1.已知数列{An}满足A1=1,An= 2A(n-1)+2(n∈N,且N≥2)(1)求A1,A2(2)设bn=An+2,证明数列{bn}是等比数列,并指出其首项和公比2.已知数列{An}满足A1=-1,An+1=2An,求该数列前十项的和S10
1.(1) A1 =1,A2 = 2*A1 + 2 = 4.
(2) b(n+1) / bn =( A(n+1)+ 2) / ( An +2)
= (2An+2 +2)/(An+2) = 2; b1 =A1+2 =3;
故bn为 首项为3,公比为2 的等比数列
2.公比2,则 S10 = -1 * (1 - 2^10)/(1-2) = -1023
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