Question

在等比数列《an》中 a2＝18 a4＝8,求a1与q 2,a5＝4 a7＝6 求a9 3,a5—a1＝15,a4—a2

Answer 1

1.a2=a1*q=18 (1)

a4=a1*q^3=8 (2)

(2)/(1) q^2=4/9

q=2/3

代入(1) a1=27

2.a5=a1*q^4=4 (3)

a7=a1*q^6=6 (4)

(4)/(3) q^2=3/2

a9=a1*q^8=(a1*q^6)*q^2=a7*q^2=6*(3/2)=9

3.a5-a1=a1*q^4-a1=a1(q^4-1)=a1*(q^2-1)(q^2+1)=15 (5)

a4-a2=a1*q^3-a1*q=a1*q(q^2-1)=6 (6)

(5)/(6) (q^2+1)/q=5/2

2q^2-5q+2=0 (2q-1)(q-2)=0

解得q=1/2或2 对应a1=-16或1

所以a3=a1*q^2=-4或4