三道等比数列填空题一起问.不是很难.
3个回答
1)
a2*a6=a3
(a1+d)*(a1+5d)=(a1+2d)^2
a1^2+6d*a1+5d^2= a1^2 + 4d*a1+4d^2
2a1*d+d^2=0
d(2a1+d)=0 ==> d=0 d=- 2a1
依题意:d= -2a1
q=a3/a2=(a1+2d)/(a1+d)=(a1-4a1)/(a1-2a1) =3
2)
an=a1*q^(n-1)=48
a(2n-1)=a1*q^(2n-2)=a1*q^[2(n-1)]=a1*[q^(n-1)]^2=192
=a1*q^(n-1)*q^(n-1)=192
==> 48*q^(n-1)=192
==> q^(n-1)=4
又 a1*q^(n-1)=48 a1=3
倒,题目没错吗?
3) a1*a9=a3*a3
a1*(a1+8d)=(a1+2d)^2
=> 4d*a1-4d^2=0
d=0 或 d=a1
依题 d=a1
a1+a2+a9=3a1+d+8d=12d
a2+a4+a10=3a1+d+3d+9d=16d
(A1+A2+A9)/(A2+A4+A10)=2/3
