等差数列{an}的前n项和为Sn,S100=100,S200=160,则S400=____________

问题描述:

等差数列{an}的前n项和为Sn,S100=100,S200=160,则S400=____________

S400-S300=S300-S200=S200-S100=60
S300=220
S400=280

S200-S100/S100=S400-S200/S200-S100

S100=a1+a2+...+a100=100S200=a1++...a200=160所以a101+a102+.a200=160-100=60得a201+a202+...a300=60*2-100=20得a301+a302+...a400=2*20-60=-20即S400=100+60+20-20=160