已知{an}为等差数列,Sn为其前n项和,a1+a5=6,S9=63 (1)求{an}的通项公式an级前n项的和Sn(2)数列{bn}满足:对∨n∈N,bn=2的an次方,求数列{an*bn}的前n项和Tn
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![已知{an}为等差数列,Sn为其前n项和,a1+a5=6,S9=63 (1)求{an}的通项公式an级前n项的和Sn(2)数列{bn}满足:对∨n∈N,bn=2的an次方,求数列{an*bn}的前n项和Tn](/uploads/image/z/7129942-70-2.jpg?t=%E5%B7%B2%E7%9F%A5%EF%BD%9Ban%EF%BD%9D%E4%B8%BA%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97%2CSn%E4%B8%BA%E5%85%B6%E5%89%8Dn%E9%A1%B9%E5%92%8C%2Ca1%2Ba5%3D6%2CS9%3D63+%EF%BC%881%29%E6%B1%82%EF%BD%9Ban%EF%BD%9D%E7%9A%84%E9%80%9A%E9%A1%B9%E5%85%AC%E5%BC%8Fan%E7%BA%A7%E5%89%8Dn%E9%A1%B9%E7%9A%84%E5%92%8CSn%EF%BC%882%EF%BC%89%E6%95%B0%E5%88%97%EF%BD%9Bbn%EF%BD%9D%E6%BB%A1%E8%B6%B3%EF%BC%9A%E5%AF%B9%E2%88%A8n%E2%88%88N%2Cbn%3D2%E7%9A%84an%E6%AC%A1%E6%96%B9%2C%E6%B1%82%E6%95%B0%E5%88%97%EF%BD%9Ban%2Abn%EF%BD%9D%E7%9A%84%E5%89%8Dn%E9%A1%B9%E5%92%8CTn)
已知{an}为等差数列,Sn为其前n项和,a1+a5=6,S9=63 (1)求{an}的通项公式an级前n项的和Sn(2)数列{bn}满足:对∨n∈N,bn=2的an次方,求数列{an*bn}的前n项和Tn
已知{an}为等差数列,Sn为其前n项和,a1+a5=6,S9=63 (1)求{an}的通项公式an级前n项的和Sn
(2)数列{bn}满足:对∨n∈N,bn=2的an次方,求数列{an*bn}的前n项和Tn
已知{an}为等差数列,Sn为其前n项和,a1+a5=6,S9=63 (1)求{an}的通项公式an级前n项的和Sn(2)数列{bn}满足:对∨n∈N,bn=2的an次方,求数列{an*bn}的前n项和Tn
(1)S9=[9*(a1+a9)]/2=[9*(2a1+8d)]/2=9(a1+4d)=63①
a1+a5=2a1+4d=6②
由①②a1=-1,d=2
所以,an=a1+(n-1)d=2n-3,Sn=[(a1+an)*n]/2=n*(n-2)
(2)bn=2的(2n-3)次方,an*bn=(2n-3)*2的(2n-3)次方
Tn=-1*2的-1次方+1*2的1次方+3*2的3次方+…+(2n-3)*2的(2n-3)次方①
4Tn=-1*2的1次方+1*2的3次方+3*2的5次方+…+(2n-3)*2的(2n-1)次方②
①-②得,-3Tn=-2的-1次方+2*(2的1次方+2的3次方+…+2的(2n-3)次方)-(2n-3)*2的(2n-1)次方 =-2的-1次方+(4-4的(2n-2)次方)/(-3)-(2n-3)*2的(2n-1)次方
等式两边除以-3得,Tn=2的-1次方/(-3)+(4-4的(2n-2)次方)/9+(2n-3)*2的(2n-1)次方/3
2a1+4d=6 9a1+36d=63 9a1+18d=27 d=2 a1=-1 an=2n-3 sn=n(n-2)