1.
(4a+3)+(a^2+8a+3)=2(7a+7)
a^2-2a-8=0
(a+2)(a-4)=0
a=-2.
2.
①
a(n+1)=a^(n+1)-2an=(-2)^(n+1)-2an
a(n+1)=(-2)^(n+1)-2an
a(n+1)/(-2)^(n+1)=1-2an/(-2)^(n+1)
=1+an/(-2)^n
a(n+1)/(-2)^(n+1)-an/(-2)^n=1
所以an/(-2)^n是公差為1,首項(xiàng)為a1/(-2)=-m/2的等差數(shù)列；
②
因a(n+1)/(-2)^(n+1)-an/(-2)^n=1
所以
an/(-2)^n=a1/(-2)+(n-1)*1
=-m/2+n-1
an=(-m/2+n-1)(-2)^n.
3.
a(2n+1)=[-m/2+(2n+1)-1](-2)^(2n+1)
=[-m/2+2n](-2)^(2n+1)
a(2n-1)=[-m/2+(2n-1)-1](-2)^(2n-1)
=[-m/2+2n-2](-2)^(2n-1)
a(2n+1)＜a(2n-1)
[-m/2+2n](-2)^(2n+1)＜[-m/2+2n-2](-2)^(2n-1)
[-2m+8n](-2)^(2n-1)＜[-m/2+2n-2](-2)^(2n-1)
-2m+8n＞-m/2+2n-2
-3m/2+6n+2＞0
n＞(3m/2-2)/6
因n≥1,只要(3m/2-2)/6＜1
所以
3m/2-2＜6
m＜16/3.