an等差数列 bn前n项和sn满足sn=3(bn-1)/2 且a2=b1 a5=b2 ⑴求an bn通项 ⑵设tn为数列
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an等差数列 bn前n项和sn满足sn=3(bn-1)/2 且a2=b1 a5=b2 ⑴求an bn通项 ⑵设tn为数列sn的前n项和,求tn
![an等差数列 bn前n项和sn满足sn=3(bn-1)/2 且a2=b1 a5=b2 ⑴求an bn通项 ⑵设tn为数列](/uploads/image/z/1595305-1-5.jpg?t=an%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97+bn%E5%89%8Dn%E9%A1%B9%E5%92%8Csn%E6%BB%A1%E8%B6%B3sn%3D3%28bn%EF%BC%8D1%29%EF%BC%8F2+%E4%B8%94a2%3Db1+a5%3Db2+%E2%91%B4%E6%B1%82an+bn%E9%80%9A%E9%A1%B9+%E2%91%B5%E8%AE%BEtn%E4%B8%BA%E6%95%B0%E5%88%97)
1.Sn=3/2bn-3/2
S(n-1)=3/2b(n-1)-3/2
bn=Sn-S(n-1)=3/2bn-3/2b(n-1)
bn=3b(n-1)
所以{bn}是等比数列,公比3
而b1=S1=3/2b1-3/2
b1=3
所以bn=3^n
a2=b1=3,a5=b2=9
d=(a5-a2)/3=2
an=2n-1
2.Sn=3/2*3^n-3/2
Tn=9/2(1-3^n)/(1-3)-3/2n=9/4(3^n-1)-3/2n
S(n-1)=3/2b(n-1)-3/2
bn=Sn-S(n-1)=3/2bn-3/2b(n-1)
bn=3b(n-1)
所以{bn}是等比数列,公比3
而b1=S1=3/2b1-3/2
b1=3
所以bn=3^n
a2=b1=3,a5=b2=9
d=(a5-a2)/3=2
an=2n-1
2.Sn=3/2*3^n-3/2
Tn=9/2(1-3^n)/(1-3)-3/2n=9/4(3^n-1)-3/2n
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