1)
a5=4,a7=6
设公比为q
q^2=a7/a5=3/2
a12=a5*q^6
=a5*(q^2)^3
=4*(3/2)^3
=4*27/8
=13.5
2)
a4-a2=24
a2+a3=6
设首项为b,公比为q;b,q都不等于0
b*q^3-b*q=24
b*q+b*q^2=6………………(1)
b*q^3-b*q=4(b*q+b*q^2)
同时除以bq,得:
q^2-1=4+4q
q^2-4q-5=0
(q+1)(q-5)=0
q=-1或q=5
bq+bq^2=6
q=-1时
-b+b=6,不接
q=5时
5b+25b=6
30b=6
b=0.2
an=b*q^(n-1)
=0.2*5^(n-1)=125
5^(n-1)=625=5^4
n-1=4
n=5