Question

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=

Answer 1

解: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.

Answer 2

你这道题有问题啊，移向后能够直接解出
an=(3+2q)/(q-1)，q是常数an也应该是常数，你看看是不是输入的时候输错了