a2/a 1=a3/a4=2,a3/a 1=2^2=4
(2a 1+a2)/(2 a3+a4)=(2a 1+2a 1)/(2 a3+2 a3)= a 1/a3 = 1/4
2.{an} is a geometric series, and let the common ratio be q.
a 1+a2+a3=7,a 1a2a3=8
a 1( 1+q+q^2)=7,a 1^3*q^3=8
a 1^3=7^3/(q^2+q+ 1)^3=8/q^3
8*(q^2+q+ 1)^3=343*q^3
2*(q^2+q+ 1)=7*q
2q^2-5q+2=0
q^2-5/2q+ 1=0
(q-5/4)^2=9/ 16
Q-5/4=3/4 or -3/4
Q=2 or 1/2
When q=2
a 1+a2+a3=7a 1=7
a 1= 1
{an} is 1 as the first term, and 2 is the common ratio sequence.
Q= 1/2
a 1+a2+a3=7/4a 1=7
a 1=4
{an} is a series with 4 as the first term and 1/2 as the common ratio.
3.a, B and C make geometric series.
A/b=b/c= radical sign (a/c)