已知等比数列{xn}的各项为不等于1的正数,数列{yn}满足yn=2logaxn(a>0且a≠1),设y3=19,y6=13.(Ⅰ
已知等比数列{xn}的各项为不等于1的正数,数列{yn}满足yn=2logaxn(a>0且a≠1),设y3=19,y6=13.(Ⅰ
日期:2016-02-19 11:37:32 人气:1
(Ⅰ)设数列{xn}的公比为q,则xn=x1qn?1,∴yn=2logaxn=2logax1qn?1=2logax1+2(n-1)logaq,∴yn-1-yn=2logax1+2nlogaq-[2logax1+2(n-1)logaq]=2logaq为常数,∴{yn}是等差数列,设公差为d,由y3=y1+2d=19y6=y1+5d=13,解得y1=23,d=-2,∴yn=23+(n-1)?(-2)=25-2n,设{yn}的前n项和为Tn,Tn=n(23+25?2n)2=-n2+24n=-(n-12)2+14