等比数列an中,Sn=2.S3n=14,求S6n(n为偶数)
问题描述:
等比数列an中,Sn=2.S3n=14,求S6n(n为偶数)
答
Sn=2,
Sn=a1(1-q^n)/(1-q)
S3n=14,
S3n=a1(1-q^3n)/(1-q)
S6n=a1(1-q^6n)/(1-q)
S3n/Sn=7
q^n=m,m为正常数,
1-m/(1-m^3)=7=m^2+m+1,->m=2,
S6n/S3n=(m^6-1)/(m^3-1)=m^3+1=9,
S6n=14*9=126