1.等比数列{an}中的前n项和为Sn,S4=2,S8=6,求S12的值2.若{an}为等差数列则Sn,S2n-Sn,S3n-S2n...也成等差数列猜想:若{an}为等比数列则Sn,S2n-Sn,S3n-S2n..也称等比数列吗?

问题描述:

1.等比数列{an}中的前n项和为Sn,S4=2,S8=6,求S12的值
2.若{an}为等差数列则Sn,S2n-Sn,S3n-S2n...也成等差数列
猜想:若{an}为等比数列则Sn,S2n-Sn,S3n-S2n..也称等比数列吗?

1.S8-S4=q^4S4
即q^4=2
S12-S8=q^8S4
则S12=14
2.设an的公比为q
S2n-Sn=q^nSn
S3n-S2n=q^2nSn
显然,Sn,S2n-Sn,S3n-S2n为公比为q^n的等比数列