设数列{an}满足关系an=3/2(an-1)+5(n≥2),a1=-17/2.令bn=an+10,求数列{bn}的前n项和Sn

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设数列{an}满足关系an=3/2(an-1)+5(n≥2),a1=-17/2.令bn=an+10,求数列{bn}的前n项和Sn

设数列{an}满足关系an=3/2(an-1)+5(n≥2),a1=-17/2.令bn=an+10,求数列{bn}的前n项和Sn
设数列{an}满足关系an=3/2(an-1)+5(n≥2),a1=-17/2.令bn=an+10,求数列{bn}的前n项和Sn

设数列{an}满足关系an=3/2(an-1)+5(n≥2),a1=-17/2.令bn=an+10,求数列{bn}的前n项和Sn
先求出an的前n项和:an=3/2an-1+5,进行变换,等价于an+10=3/2(an-1+10),即可得
{an+10}是等比数列,公比1.5,首项为1.5
所以bn=1.5的n次方
sn=3-3*(1.5的n次方)

因为2an=3/2(an-1)+5(n≥2)两边都加10得到an+10=3/2*[(an-1)+10].....(1)
因为bn=an+10,所以bn-1(n-1是下标,下同)=an-1+10
由(1)得bn=3/2*bn-1(n≥2),所以数列bn是以b1=a1+10=3/2,公比是3/2的等比数列,Sn=b1(1-q^n)/(1-q)代入b1=q=3/2得到Sn=3^(n+1)2^n -3

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