设公差不为0的等差数列an的首项为1,且a6=a2^2,求数列an的通项公式,若bn满足bn=nan+5n,求{1/bn

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设公差不为0的等差数列an的首项为1,且a6=a2^2,求数列an的通项公式,若bn满足bn=nan+5n,求{1/bn}的前n项和Tn

an=a1+(n-1)d
a1=1
a6= (a2)^2
(1+5d) = (1+d)^2
d^2-3d=0
d=3
an = 1+3(n-1) = 3n-2
bn=nan+5n
= n(3n-2) + 5n
= 3n(n+1)
1/bn = 1/[3n(n+1)]
= (1/3)[1/n -1/(n+1) ]
Tn = 1/b1+1/b2+...+1/bn
= (1/3)[1-1/(n+1) ]
=n/[3(n+1)]

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