已知数列{an}满足an+1=qan+2q-2,(q为常数）,若a3,a4,a5,a6∈{﹣18,﹣6,6,30},则a

来源：学生作业帮编辑：大师作文网作业帮分类：数学作业时间：2024/11/11 01:47:10

已知数列{an}满足an+1=qan+2q-2,(q为常数）,若a3,a4,a5,a6∈{﹣18,﹣6,6,30},则a1=

a6=q*a5+2q-2,
a5=q*a4+2q-2,
a4=q*a3+2q-2,
a3=q*a2+2q-2,
所以a6+2=q(a5+2),
a5+2=q(a4+2),
a4+2=q(a3+2),
即a3+2,a4+2,a5+2,a6+2成等比数列,
因a3,a4,a5,a6∈(-18,-6,6,30),
所以a3+2,a4+2,a5+2,a6+2∈(-16,-4,8,32),
q=-2,a3+2=-4,a4+2=8,a5+2=-16,a6+2=32或q=-1/2,a3+2=32,a4+2=-16,a5+2=8,a6+2=-4
即q=-2,a3=-6,a4=6,a5=-18,a6=30或q=-1/2,a3=30,a4=-18,a5=6,a6=-6.
a2+2=(a3+2)/q=2,a2=0,a1+2=(a2+2)/q=-1,a1=-3
或a2+2=(a3+2)/q=-64,a2=-66,a1+2=(a2+2)/q=128,a1=126
所以a1=-3或126.

等比数列{an}中,已知a1+a2+a3=1/2,a4+a5+a6=-4,则公比q为多少? 等比数列{an}中,a1+a2+a3=1 a4+a5+a6=-2 则公比q为多少? 等比数列an的公比为q,（1）若a3=-4,a6=54,求a9（2）a5=4,a7=6,求a9 (3)a2=18,a4= 如果数列an满足a{n+1}=pan+q(p,q为常数）,则称an为"H数列".已知数列an的前n项和为Sn,若Sn=2 已知等比数列{an}的公比q= -1/3,则(a1+a3+a5+a7)/(a2+a4+a6+a8)等于多少已知等比数列an的公比q=1/3,则a1+a3+a5+a7/a2+a4+a6+a8等于已知等比数列{an}的公笔q=-1/3,则a1+a3+a5+a7/a2+a4+a6+a8等于? 已知等比数列{an}的公比q=-13，则a1+a3+a5+a7a2+a4+a6+a8等于（　　）已知数列{an}满足A1=0,A(N+1)=AN减去根号三/根号三AN加1.求A2,A3,A4,A5,A6 已知数列(an)满足a1=1,an+1=2an/an+2(n∈N*) 求a2,a3,a4,a5 猜想数列(an)的通项公已知an是等比数列,且an>0,a2*a4+2a3*a5+a4*a6=25,则a3+a5=? 已知数列{an},a1=2a6=17,求a2+a3+a4+a5