an数列an的前n项和为sn,数列bn的前n项和为Tn,bn为等差数列且各项均为正数,a1=1,a(n+1)=2sn+1,T3=15.求证数列an是等比数列 (2)若a1+b1,a2+b2,a3+b3成等比数列,求Tn
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![an数列an的前n项和为sn,数列bn的前n项和为Tn,bn为等差数列且各项均为正数,a1=1,a(n+1)=2sn+1,T3=15.求证数列an是等比数列 (2)若a1+b1,a2+b2,a3+b3成等比数列,求Tn](/uploads/image/z/8819409-57-9.jpg?t=an%E6%95%B0%E5%88%97an%E7%9A%84%E5%89%8Dn%E9%A1%B9%E5%92%8C%E4%B8%BAsn%2C%E6%95%B0%E5%88%97bn%E7%9A%84%E5%89%8Dn%E9%A1%B9%E5%92%8C%E4%B8%BATn%2Cbn%E4%B8%BA%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97%E4%B8%94%E5%90%84%E9%A1%B9%E5%9D%87%E4%B8%BA%E6%AD%A3%E6%95%B0%2Ca1%3D1%2Ca%28n%2B1%29%3D2sn%2B1%2CT3%3D15.%E6%B1%82%E8%AF%81%E6%95%B0%E5%88%97an%E6%98%AF%E7%AD%89%E6%AF%94%E6%95%B0%E5%88%97+%EF%BC%882%EF%BC%89%E8%8B%A5a1%2Bb1%2Ca2%2Bb2%2Ca3%2Bb3%E6%88%90%E7%AD%89%E6%AF%94%E6%95%B0%E5%88%97%2C%E6%B1%82Tn)
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an数列an的前n项和为sn,数列bn的前n项和为Tn,bn为等差数列且各项均为正数,a1=1,a(n+1)=2sn+1,T3=15.求证数列an是等比数列 (2)若a1+b1,a2+b2,a3+b3成等比数列,求Tn
an数列an的前n项和为sn,数列bn的前n项和为Tn,bn为等差数列且各项均为正数,a1=1,a(n+1)=2sn+1,T3=15.求证数
列an是等比数列 (2)若a1+b1,a2+b2,a3+b3成等比数列,求Tn
an数列an的前n项和为sn,数列bn的前n项和为Tn,bn为等差数列且各项均为正数,a1=1,a(n+1)=2sn+1,T3=15.求证数列an是等比数列 (2)若a1+b1,a2+b2,a3+b3成等比数列,求Tn
(1)因为a(n+1)=2sn+1
所以Sn=[a(n+1)-1]/2
an=Sn-Sn-1=[a(n+1)-an]/2
a(n+1)=3an等比数列
(2)a1=1,a2=3,a3=9
设{bn}的公差为d
则(3+b2)^2=(1+b2-d)(9+b2+d)
T3=3b2=15
根据以上两式得b2=5 d=-10(舍去)或d=2
所以b1=3
Tn=nb1+d/2*n(n-1)=3n+n(n-1)=n^2+2n