第二小问
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解:(Ⅰ)由an+1>an,可得公差d>0
∵a2a9=232,a4+a7=a2+a9=37
∴a9>a2
∴ a2=8 a9=29
设公差为d,则d=a9−a2 9−2 =29−8 9−2 =3
∴an=a2+3(n-2)=8+3n-6=3n+2…
(Ⅱ)由题意得:bn=a2n−1+a2n−1+1 +…+a2n−1+2n−1−1,
=(3•2n-1+2)+(3•2n-1+5)+(3•2n-1+8)+…+[3•2n-1+(3•2n-1-1)]
=2n-1×3•2n-1+[2+5+8+…+(3•2n-1-4)+(3•2n-1-1)]…
而2+5+8+…+(3•2n-1-4)+(3•2n-1+1)是首项为2,公差为3的等差数列的2n-1项的和,
所以2+5+8+…++(3•2n-1-4)+(3•2n-1-1)=2n−1×2+2n−1(2n−1−1) 2 ×3
=3•22n−3+2n 4
所以bn=3•22n−2+3•22n−3+2n 4 …
所以bn−1 4 •2n=
∵a2a9=232,a4+a7=a2+a9=37
∴a9>a2
∴ a2=8 a9=29
设公差为d,则d=a9−a2 9−2 =29−8 9−2 =3
∴an=a2+3(n-2)=8+3n-6=3n+2…
(Ⅱ)由题意得:bn=a2n−1+a2n−1+1 +…+a2n−1+2n−1−1,
=(3•2n-1+2)+(3•2n-1+5)+(3•2n-1+8)+…+[3•2n-1+(3•2n-1-1)]
=2n-1×3•2n-1+[2+5+8+…+(3•2n-1-4)+(3•2n-1-1)]…
而2+5+8+…+(3•2n-1-4)+(3•2n-1+1)是首项为2,公差为3的等差数列的2n-1项的和,
所以2+5+8+…++(3•2n-1-4)+(3•2n-1-1)=2n−1×2+2n−1(2n−1−1) 2 ×3
=3•22n−3+2n 4
所以bn=3•22n−2+3•22n−3+2n 4 …
所以bn−1 4 •2n=
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