Question

a5-a1=15,a4-a2=6.等比数列 求a3

Answer 1

a5-a1=a1q^4-a1=a1(q^4-1)=a1(q^2+1)(q^2-1)=15

a4-a2=a1q^3-a1q=a1q(q^2-1)=6

相除

(q^2+1)/q=15/6

2q^2-5q+2=0

q=2,q=1/2

q=2,a1(q^4-1)=15,a1=1,a3=a1q^2=4

q=1/2,a1(q^4-1)=15,a1=-16,a3=a1q^2=-4

所以a3=4或-4