已知{An}是一个公差大于0的等差数列,且满足a3a5=55,a2+a7=16:(1).数列{An}的通项数列;(2)若数列{An}和数列{bn}满足等式:An=(B1/2)+(B2/2^2)+(B3/2^3)+.+(Bn/2^n),n∈N*,求数列{Bn}的前n项和Sn
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![已知{An}是一个公差大于0的等差数列,且满足a3a5=55,a2+a7=16:(1).数列{An}的通项数列;(2)若数列{An}和数列{bn}满足等式:An=(B1/2)+(B2/2^2)+(B3/2^3)+.+(Bn/2^n),n∈N*,求数列{Bn}的前n项和Sn](/uploads/image/z/1761650-26-0.jpg?t=%E5%B7%B2%E7%9F%A5%EF%BD%9BAn%EF%BD%9D%E6%98%AF%E4%B8%80%E4%B8%AA%E5%85%AC%E5%B7%AE%E5%A4%A7%E4%BA%8E0%E7%9A%84%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97%2C%E4%B8%94%E6%BB%A1%E8%B6%B3a3a5%3D55%2Ca2%2Ba7%3D16%EF%BC%9A%281%29.%E6%95%B0%E5%88%97%7BAn%7D%E7%9A%84%E9%80%9A%E9%A1%B9%E6%95%B0%E5%88%97%EF%BC%9B%EF%BC%882%EF%BC%89%E8%8B%A5%E6%95%B0%E5%88%97%7BAn%7D%E5%92%8C%E6%95%B0%E5%88%97%7Bbn%7D%E6%BB%A1%E8%B6%B3%E7%AD%89%E5%BC%8F%EF%BC%9AAn%3D%EF%BC%88B1%2F2%EF%BC%89%2B%EF%BC%88B2%2F2%5E2%EF%BC%89%2B%EF%BC%88B3%2F2%5E3%EF%BC%89%2B.%2B%28Bn%2F2%5En%29%2Cn%E2%88%88N%2A%2C%E6%B1%82%E6%95%B0%E5%88%97%EF%BD%9BBn%EF%BD%9D%E7%9A%84%E5%89%8Dn%E9%A1%B9%E5%92%8CSn)
已知{An}是一个公差大于0的等差数列,且满足a3a5=55,a2+a7=16:(1).数列{An}的通项数列;(2)若数列{An}和数列{bn}满足等式:An=(B1/2)+(B2/2^2)+(B3/2^3)+.+(Bn/2^n),n∈N*,求数列{Bn}的前n项和Sn
已知{An}是一个公差大于0的等差数列,且满足a3a5=55,a2+a7=16:
(1).数列{An}的通项数列;(2)若数列{An}和数列{bn}满足等式:An=(B1/2)+(B2/2^2)+(B3/2^3)+.+(Bn/2^n),n∈N*,求数列{Bn}的前n项和Sn.
已知{An}是一个公差大于0的等差数列,且满足a3a5=55,a2+a7=16:(1).数列{An}的通项数列;(2)若数列{An}和数列{bn}满足等式:An=(B1/2)+(B2/2^2)+(B3/2^3)+.+(Bn/2^n),n∈N*,求数列{Bn}的前n项和Sn
1.a3a5=55,a2+a7=16=a3+a5
那么联立解得a3=5 a5=11那么d=3 a1=-1
An=3n-4
2.3n-4=(B1/2)+(B2/2^2)+(B3/2^3)+.+(Bn/2^n),n∈N*
我们在写一项3(n+1)-4=(B1/2)+(B2/2^2)+(B3/2^3)+.+(Bn/2^n)+(Bn+1)/2^(n+1))
那么下式减上式得3=(Bn+1)/2^(n+1))
那么Bn+1=3*2^(n+1)
那么Bn=3*2^n
Sn=3*2*(2^n-1)=6*(2^n-1)
a2+a7=2a4=16
a4=8
a3a5=(a4+d)(a4-d)=64-d^2=55
d=3
a1=a4-3d=-1
an=3n-4
解∶(1)(a1+2d)(a1+4d)=55 a1+d+a1+6d=16 可解得答案