Question

设等比数列｛an｝共有3n项,它的前2n项的和为100,后2n项的和为200,则该等比数列中间n项的和为多少?

Answer 1

S2n=100,a1(1-q^2n)/(1-q)=100

S3n-Sn=200,a1(q^n-q^3n)/(1-q)=200

得q^n=2

S2n=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

中间n项=100-100/3