已知等差数列{an}的各项均为正数,a1=3,前n项和为Sn,{bn}是等比数列,公比q=2,且a2b2=20,a3b3=56(1)求an与bn (2)求数列{anbn}的前n项和Tn 过程希望详细点,急!
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![已知等差数列{an}的各项均为正数,a1=3,前n项和为Sn,{bn}是等比数列,公比q=2,且a2b2=20,a3b3=56(1)求an与bn (2)求数列{anbn}的前n项和Tn 过程希望详细点,急!](/uploads/image/z/978472-64-2.jpg?t=%E5%B7%B2%E7%9F%A5%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97%7Ban%7D%E7%9A%84%E5%90%84%E9%A1%B9%E5%9D%87%E4%B8%BA%E6%AD%A3%E6%95%B0%2Ca1%3D3%2C%E5%89%8Dn%E9%A1%B9%E5%92%8C%E4%B8%BASn%2C%7Bbn%7D%E6%98%AF%E7%AD%89%E6%AF%94%E6%95%B0%E5%88%97%2C%E5%85%AC%E6%AF%94q%3D2%2C%E4%B8%94a2b2%3D20%2Ca3b3%3D56%EF%BC%881%EF%BC%89%E6%B1%82an%E4%B8%8Ebn+%282%29%E6%B1%82%E6%95%B0%E5%88%97%7Banbn%7D%E7%9A%84%E5%89%8Dn%E9%A1%B9%E5%92%8CTn+%E8%BF%87%E7%A8%8B%E5%B8%8C%E6%9C%9B%E8%AF%A6%E7%BB%86%E7%82%B9%2C%E6%80%A5%21)
已知等差数列{an}的各项均为正数,a1=3,前n项和为Sn,{bn}是等比数列,公比q=2,且a2b2=20,a3b3=56(1)求an与bn (2)求数列{anbn}的前n项和Tn 过程希望详细点,急!
已知等差数列{an}的各项均为正数,a1=3,前n项和为Sn,{bn}是等比数列,公比q=2,且a2b2=20,a3b3=56(1)求an与bn (2)求数列{anbn}的前n项和Tn
过程希望详细点,急!
已知等差数列{an}的各项均为正数,a1=3,前n项和为Sn,{bn}是等比数列,公比q=2,且a2b2=20,a3b3=56(1)求an与bn (2)求数列{anbn}的前n项和Tn 过程希望详细点,急!
(1) an=a1+(n-1)d=3+(n-1)d
bn=b1*q^(n-1)=b1*2^(n-1)
a2b2=(3+d)*2b1=20
a3b3=(3+2d)*4b1=56
d=2 b1=2
an=2n+1
bn=2^n
(2) anbn=(2n+1)*2^n
Tn=3*2+5*2^2+7*2^3+...+(2n+1)*2^n
2Tn=3*2^2+5*2^3+...+(2n-1)*2^n+(2n+1)*2^(n+1)
Tn-2Tn=3*2+2(2^2+2^3+...+2^n)-(2n+1)*2^(n+1)
-Tn=6+8[1-2^(n-1)]/(1-2)-(2n+1)*2^(n+1)
Tn=(2n+1)*2^(n+1)-6+8-2*2^(n+1)
=(2n-1)*2^(n+1)+2