Question

已知数列{an}为等比数列,Sn为前几项之和 若S3S5-S4^2=-16,a2a4=32求S4的值

Answer 1

an=a1q^(n-1)

a2a4=32

a1q*a1q^3=32

a1^2*q^4=32

Sn=a1(1-q^n)(/1-q)

S3S5-S4^2=-16

a1^2/(1-q)^2((1-q^3)(1-q^5)-(1-q^4)^2）=-16

-a1^2*q^3=-16

a1^2*q^3=16

a1^2*q^4=32

q=2

a1=±√2

S4==±15√2