Question

数列{an}是等比数列,若a1+a2+a3= - 3,a1a2a3=8,则an=?

Answer 1

a1a2a3=8

(a2)^3=8

a2=2

a1+a2+a3=-3

a1+2+a3=-3

a1+a3=-5

a2/q+a2q=-5

2/q+2q+5=0

2q^2+5q+2=0

(2q+1)(q+2)=0

q=-1/2或q=-2

当q=-1/2时

a2=a1q

2=a1*(-1/2)

a1=-4

an=a1q^(n-1)

an=-4*(-1/2)^(n-1)

an=-(-1/2)^(-2)*(-1/2)^(n-1)

an=-(-1/2)^(n-3)