設等比數列{an}共有3n項,它的前2n項的和為100,後2n項的和為200,則該等比數列中間n項的和為多少?

設等比數列{an}共有3n項,它的前2n項的和為100,後2n項的和為200,則該等比數列中間n項的和為多少?

S2n=100,a1(1-q^2n)/(1-q)=100S3n-Sn=200,a1(q^n-q^3n)/(1-q)=200得q^n=2S2n=100=a1(1-q^2n)/(1-q)=a1(1+q^n)(1-q^n)/(1-q)=(1+q^n)Sn=3Sn故Sn=100/3中間n項=100-100/3