.已知等差数列{an}公差d不等于0,它的前n项和为sn,若s5=70,且a2,a7,a22成等比数列(1)求{an}的通项公式(2数列{sn分之1}的前n项和为Tn,求证6分之1≤Tn＜8分之3

题目

.已知等差数列{an}公差d不等于0,它的前n项和为sn,若s5=70,且a2,a7,a22成等比数列(1)求{an}的通项公式(2数列{sn分之1}的前n项和为Tn,求证6分之1≤Tn＜8分之3

答案

(1)an = a1+(n-1)dS5=70(a1+2d)5 = 70a1+2d = 14 (1)a2,a7,a22成等比数列a2.a22= (a7)^2(a1+d)(a1+21d)=(a1+6d)^2(14-d)(14+19d)=(14+4d)^2 ( from (1) :a1+2d=14)196+252d-19d^2= 196+112d+16d^235d^2-140d=0d^2-4d...