.已知 {an} 是等差数列.(1)前4项和为21,末4项和为67,且各项和为286.求项数; (2).已知 {an} 是等差数列.(1)前4项和为21,末4项和为67,且各项和为286.求项数; (2) ,求 ; (3)项数为奇数,奇数项和为44,偶数项
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![.已知 {an} 是等差数列.(1)前4项和为21,末4项和为67,且各项和为286.求项数; (2).已知 {an} 是等差数列.(1)前4项和为21,末4项和为67,且各项和为286.求项数; (2) ,求 ; (3)项数为奇数,奇数项和为44,偶数项](/uploads/image/z/3985346-2-6.jpg?t=.%E5%B7%B2%E7%9F%A5+%7Ban%7D+%E6%98%AF%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97.%281%29%E5%89%8D4%E9%A1%B9%E5%92%8C%E4%B8%BA21%2C%E6%9C%AB4%E9%A1%B9%E5%92%8C%E4%B8%BA67%2C%E4%B8%94%E5%90%84%E9%A1%B9%E5%92%8C%E4%B8%BA286.%E6%B1%82%E9%A1%B9%E6%95%B0%3B+%282%29%EF%BC%8E%E5%B7%B2%E7%9F%A5+%7Ban%7D+%E6%98%AF%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97.%281%29%E5%89%8D4%E9%A1%B9%E5%92%8C%E4%B8%BA21%2C%E6%9C%AB4%E9%A1%B9%E5%92%8C%E4%B8%BA67%2C%E4%B8%94%E5%90%84%E9%A1%B9%E5%92%8C%E4%B8%BA286.%E6%B1%82%E9%A1%B9%E6%95%B0%3B+%282%29+%2C%E6%B1%82+%3B+%283%29%E9%A1%B9%E6%95%B0%E4%B8%BA%E5%A5%87%E6%95%B0%2C%E5%A5%87%E6%95%B0%E9%A1%B9%E5%92%8C%E4%B8%BA44%2C%E5%81%B6%E6%95%B0%E9%A1%B9)
.已知 {an} 是等差数列.(1)前4项和为21,末4项和为67,且各项和为286.求项数; (2).已知 {an} 是等差数列.(1)前4项和为21,末4项和为67,且各项和为286.求项数; (2) ,求 ; (3)项数为奇数,奇数项和为44,偶数项
.已知 {an} 是等差数列.(1)前4项和为21,末4项和为67,且各项和为286.求项数; (2)
.已知 {an} 是等差数列.(1)前4项和为21,末4项和为67,且各项和为286.求项数; (2) ,求 ; (3)项数为奇数,奇数项和为44,偶数项和为33,求数列的中间项和项数.
.已知 {an} 是等差数列.(1)前4项和为21,末4项和为67,且各项和为286.求项数; (2).已知 {an} 是等差数列.(1)前4项和为21,末4项和为67,且各项和为286.求项数; (2) ,求 ; (3)项数为奇数,奇数项和为44,偶数项
a1+a2+a3+a4=21
an+a(n-1)+a(n-2)+a(n-3)=67
--->(a1+an)+[a2+a(n-1)]+[a3+a(n-2)+[a4+a(n-3)]=88
--->4(a1+an)=88
--->a1+an=22
因此Sn=n(a1+an)/2=11n
又Sn=286,所以11n=286
所以 n=26.
设等差数列{an}项数为2n+1,
S奇=a1+a2+a3+…a2n+1=(n+1)(a1+a2n+1)/2=(n+1)an+1,
S偶=a2+a4+a6+…a2n=n(a2+a2n)/2=nan+1,
∴S奇/S偶=n+1/n=44/33,
n=3,
∴项数2n+1=7,
又因为S奇-S偶=an+1=a中,
所以a4=S奇-S偶=44-33=11,
所以中间项为11.