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

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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.

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