等比数列{an}的前n项和为10,前2n项和为30,求前3n项和

Question

等比数列{an}的前n项和为10,前2n项和为30,求前3n项和

Answer 1

sn=a1(1-q^n)/(1-q)=10
s2n=a1(1-q^2n)/(1-q)=30
sn/s2n=(1-q^n)/(1-q^2n)=1/3
设q^n=x
(1-x)/(1-x^2)=1/3
x=1(舍去),x=2
所以q^n=2
s3n=a1(1-q^3n)/(1-q)
sn/s3n=(1-q^n)/(1-q^3n)=(1-2)/(1-2^3)=1/7
s3n=7*10=70