问题
填空题
等差数列前m项和是30,前2m项和是100,则它的前3m项和是______.
答案
依题意,Sm,S2m-Sm,S3m-S2m成等差数列.
即30,70,S3m-100成等差数列.
∴30+S3m-100=2×70
∴Sm=210.
等差数列前m项和是30,前2m项和是100,则它的前3m项和是______.
依题意,Sm,S2m-Sm,S3m-S2m成等差数列.
即30,70,S3m-100成等差数列.
∴30+S3m-100=2×70
∴Sm=210.