设{an}为等比数列,(1)已知a1=7,a4=-56,求a5和s5 (2)已知a1=3,an=96,sn=189,求q和n(过程)
问题描述:
设{an}为等比数列,(1)已知a1=7,a4=-56,求a5和s5 (2)已知a1=3,an=96,sn=189,求q和n(过程)
答
(1){an}为等比数列a1=7,a4=a1q^3=-56,
∴q=-2
∴a5=a1q^4=56,
sn=a1(1-q^n)/(1-q)=7[1-(-2)^n]/3
∴s5=67
(2)an=a1q^(n-1)=96,①
sn=a1(1-q^n)/(1-q)=189②
解方程组得:n= 6,q= 2