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    已知數(shù)列{an}是公差為d的等差數(shù)列.d≠0且a1=0,bn=2 (n∈N*),Sn是{bn}的前n項和.Tn= (n∈N*).(1)求{Tn}的通項公式, 查看更多

     

    題目列表(包括答案和解析)

    已知數(shù)列{an}是公差為d的等差數(shù)列,且d≠0,數(shù)列{bn}是公比為q的等比數(shù)列,且a1=1,a2=b1,a5=b2,a14=b3,則d=
     
    ,q=
     

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    已知數(shù)列{an}是公差為d的等差數(shù)列,S1=
    n
    i=1
    ai,S2=an+1+an+2+…+a2n,s3=a2n+1+a2n+2+…+a3n,則數(shù)列S1,S2,S3的公差為( 。

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    已知數(shù)列{an}是公差為d的等差數(shù)列,Sn是其前n項和,且有S9<S8=S7,則下列說法不正確的是( 。

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    已知數(shù)列{an}是公差為d的等差數(shù)列,且各項均為正整數(shù),如果a1=1,an=16,那么n+d的最小值為
    9
    9

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    已知數(shù)列{an}是公差為d的等差數(shù)列,且d≠0,數(shù)列{bn}是公比為q的等比數(shù)列,且a1=1,a2=b1,a5=b2,a14=b3,則d=______________,q=______________.

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    難點磁場

    6ec8aac122bd4f6e

    殲滅難點訓(xùn)練

    一、1.解析:6ec8aac122bd4f6e,

    6ec8aac122bd4f6e

    答案:A

    2.解析:6ec8aac122bd4f6e

    答案:C

    二、3.解析:6ec8aac122bd4f6e

    6ec8aac122bd4f6e

    答案:6ec8aac122bd4f6e

    4.解析:原式=6ec8aac122bd4f6e

    6ec8aac122bd4f6e

    a?b=86ec8aac122bd4f6e

    答案:86ec8aac122bd4f6e

    三、5.解:(1)由{an+16ec8aac122bd4f6ean}是公比為6ec8aac122bd4f6e的等比數(shù)列,且a1=6ec8aac122bd4f6e,a2=6ec8aac122bd4f6e,

    an+16ec8aac122bd4f6ean=(a26ec8aac122bd4f6ea1)(6ec8aac122bd4f6e)n-1=(6ec8aac122bd4f6e6ec8aac122bd4f6e×6ec8aac122bd4f6e)(6ec8aac122bd4f6e)n-1=6ec8aac122bd4f6e,

    an+1=6ec8aac122bd4f6ean+6ec8aac122bd4f6e                                               ①

    又由數(shù)列{lg(an+16ec8aac122bd4f6ean)}是公差為-1的等差數(shù)列,且首項lg(a26ec8aac122bd4f6ea1)

    =lg(6ec8aac122bd4f6e6ec8aac122bd4f6e×6ec8aac122bd4f6e)=-2,

    ∴其通項lg(an+16ec8aac122bd4f6ean)=-2+(n-1)(-1)=-(n+1),

    an+16ec8aac122bd4f6ean=10(n+1),即an+1=6ec8aac122bd4f6ean+10(n+1)                                                                                                

    ①②聯(lián)立解得an=6ec8aac122bd4f6e[(6ec8aac122bd4f6e)n+1-(6ec8aac122bd4f6e)n+1

    (2)Sn=6ec8aac122bd4f6e

    6ec8aac122bd4f6e

    6.解:由于6ec8aac122bd4f6e=1,可知,f(2a)=0                                                                      ①

    同理f(4a)=0                                                                                                            ②

    由①②可知f(x)必含有(x-2a)與(x-4a)的因式,由于f(x)是x的三次多項式,故可設(shè)f(x)=A(x-2a)(x-4a)(xC),這里A、C均為待定的常數(shù),

    6ec8aac122bd4f6e

    6ec8aac122bd4f6e,即4a2A-2aCA=-1                                                         ③

    同理,由于6ec8aac122bd4f6e=1,得A(4a-2a)(4aC)=1,即8a2A-2aCA=1                        ④

    由③④得C=3a,A=6ec8aac122bd4f6e,因而f(x)= 6ec8aac122bd4f6e (x-2a)(x-4a)(x-3a),

    6ec8aac122bd4f6e

    6ec8aac122bd4f6e

    由數(shù)列{an}、{bn}都是由正數(shù)組成的等比數(shù)列,知p>0,q>0

    6ec8aac122bd4f6e

    當(dāng)p<1時,q<1, 6ec8aac122bd4f6e

    6ec8aac122bd4f6e

    8.解:(1)an=(n-1)d,bn=26ec8aac122bd4f6e=2(n1)d?

    Sn=b1+b2+b3+…+bn=20+2d+22d+…+2(n1)d?

    d≠0,2d≠1,∴Sn=6ec8aac122bd4f6e

    Tn=6ec8aac122bd4f6e

    (2)當(dāng)d>0時,2d>1

    6ec8aac122bd4f6e

     

     

     


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