等差数列{an}的前n项和为Sn,若Sn=30,S2n=100,则S3n=( ) A.130 B.170 C.210 D.260
问题描述:
等差数列{an}的前n项和为Sn,若Sn=30,S2n=100,则S3n=( )
A. 130
B. 170
C. 210
D. 260
答
因为数列{an}为等差数列,
所以由等差数列性质可得:sn,s2n-sn,s3n-s2n…为等差数列.
即30,100-30,S3n-100是等差数列,
∴2×70=30+S3n-100,解得S3n=210,
故选C.