等差数列{an}的公差不为零,a4=7,a1,a2,a5成等比数列. 若数列{Tn}满足Tn=a2+a4+a8+…+a2n,求Tn.

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问题 等差数列{an}的公差不为零,a4=7,a1,a2,a5成等比数列.
若数列{Tn}满足Tn=a2+a4+a8+…+a2n,求Tn.

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答案Tn=a2+a4+a8+…+a2n =(2×2—1)+(2×22一1)+(2×23一1)+…+(2×2n一1) =2×(2+22+23+…+2n)一n =[*] =2n+2一n—4.

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