等差数列的前n项和 习题等差数列{an}的前m项和为30,前2m项和为100,则它的前3m项的和为多少?
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等差数列的前n项和 习题等差数列{an}的前m项和为30,前2m项和为100,则它的前3m项的和为多少?
等差数列的前n项和 习题
等差数列{an}的前m项和为30,前2m项和为100,则它的前3m项的和为多少?
等差数列的前n项和 习题等差数列{an}的前m项和为30,前2m项和为100,则它的前3m项的和为多少?
若an为等差数列,则sn,s2n-sn,s3n-s2n.也为等差数列
所以sm,s2m-sm,s3m-s2m为30,70,110
所以设s3m=30+70+110=210
Sm=a1+(m-1)d=30,
S2m=a1+(2m-1)d=100;
S2m-Sm=md=70,
故S3m=a1+(3m-1)d=a1+(m-1)d+2md=30+2*70=170
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