已知SN是等差数列,S6=36,SN=324,S(N-6)=144,则N=?
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已知SN是等差数列,S6=36,SN=324,S(N-6)=144,则N=?
![已知SN是等差数列,S6=36,SN=324,S(N-6)=144,则N=?](/uploads/image/z/16339800-48-0.jpg?t=%E5%B7%B2%E7%9F%A5SN%E6%98%AF%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97%2CS6%3D36%2CSN%3D324%2CS%28N-6%29%3D144%2C%E5%88%99N%3D%3F)
Sn-S
=a+a+……+an
=324-144
=180
S6=a6+a5+……+a1=36
两式相加得
(a+a6)+(a+a5)+……+(an+a1)=180+36
6(a1+an)=216
a1+an=36
Sn=n(a1+an)/2=324
n*36/2=324
n=18
=a+a+……+an
=324-144
=180
S6=a6+a5+……+a1=36
两式相加得
(a+a6)+(a+a5)+……+(an+a1)=180+36
6(a1+an)=216
a1+an=36
Sn=n(a1+an)/2=324
n*36/2=324
n=18
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