数列an的前n项和sn满足sn=2an-1,等差数列bn满足b1=a1 b4=s3求an an 桐乡...数列an的前n项和sn满足sn=2an-1,等差数列bn满足b1=a1 b4=s3求an an 桐乡公式
问题描述:
数列an的前n项和sn满足sn=2an-1,等差数列bn满足b1=a1 b4=s3求an an 桐乡...
数列an的前n项和sn满足sn=2an-1,等差数列bn满足b1=a1 b4=s3求an an 桐乡公式
答
∵sn-s(n-1)=an ∴2an-1-[2a(n-1)-1]=an ∴an=2a(n-1) ∴an/a(n-1)=2
∴an为等比数例 ∵sn=2an-1 ∴a1=2a1-1 ∴a1=1
∴an=a1×q^(n-1)=2^(n-1)
∵等差数列bn满足b1=a1 b4=s3
∴b1=a1=1 b4=s3=2a3-1=2×4-1=7=b1+3d=1+3d ∴d=2
∴bn=1+2(n-1)=2n-1