等差数列{an}中,a100,且a10的绝对值>a11的绝对值,Sn 为数列{an}的前n项和,则()A S1,S2...S10都小于0,S11,S12...都大于0 B S1,S2...S19都小于0,S20,S21...都大于0 C S1,S2...S5都小于0,S6,S7...都大于0 D S1,S2...S20都小
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等差数列{an}中,a100,且a10的绝对值>a11的绝对值,Sn 为数列{an}的前n项和,则()A S1,S2...S10都小于0,S11,S12...都大于0 B S1,S2...S19都小于0,S20,S21...都大于0 C S1,S2...S5都小于0,S6,S7...都大于0 D S1,S2...S20都小
等差数列{an}中,a100,且a10的绝对值>a11的绝对值,Sn 为数列{an}的前n项和,则()
A S1,S2...S10都小于0,S11,S12...都大于0
B S1,S2...S19都小于0,S20,S21...都大于0
C S1,S2...S5都小于0,S6,S7...都大于0
D S1,S2...S20都小于0,S21,S22...都大于0
等差数列{an}中,a100,且a10的绝对值>a11的绝对值,Sn 为数列{an}的前n项和,则()A S1,S2...S10都小于0,S11,S12...都大于0 B S1,S2...S19都小于0,S20,S21...都大于0 C S1,S2...S5都小于0,S6,S7...都大于0 D S1,S2...S20都小
解析,
a100,
又,|a10|>|a11|,
-a10>a11,
故,a10+a11
D
根据a10<0,a11>0,且a10的绝对值>a11的绝对值有
a10+a11<0,
a1+a20=a2+a19=....=a10+a11
S20=a1+a2+a3+.....+a19+a20=10*(a10+a11)<0
据排他法只有D符合
d=a11-a10>0 故an为增
由题意a10+a11<0
故s20=(a1+a20)*20/2=(a10+a11)*20/2<0
s21=(a1+a21)*21/2=2a11*21/2>0
故选D