已知数列{an}满足a2=3,an-2+an-1+an=51(n大于3),Sn=100,则n的值为?
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![已知数列{an}满足a2=3,an-2+an-1+an=51(n大于3),Sn=100,则n的值为?](/uploads/image/z/373565-29-5.jpg?t=%E5%B7%B2%E7%9F%A5%E6%95%B0%E5%88%97%7Ban%7D%E6%BB%A1%E8%B6%B3a2%3D3%2Can-2%2Ban-1%2Ban%3D51%28n%E5%A4%A7%E4%BA%8E3%29%2CSn%3D100%2C%E5%88%99n%E7%9A%84%E5%80%BC%E4%B8%BA%3F)
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已知数列{an}满足a2=3,an-2+an-1+an=51(n大于3),Sn=100,则n的值为?
已知数列{an}满足a2=3,an-2+an-1+an=51(n大于3),Sn=100,则n的值为?
已知数列{an}满足a2=3,an-2+an-1+an=51(n大于3),Sn=100,则n的值为?
n=10 设该数列为等差数列
由an-2+an-1+an=51可知an-1=51/3=17
那么 a2+an-1=17+3=20
又Sn=n/2*(a1+an)=n/2*(a2+an-1)=100
解之得n=10.
an-2=an-(n-1)-(n-2)
=an-2n+3
an-1=an-(n-1)
=an-n-1
因为an-2+an-1+an=51
所以an-2n+3+an-n-1+an=51
an=(3n-49)/3
sn=a1+a2+a3+...an-2+an-1+an=100
an-2+an-1+an=51(n大于3)
所以n=17
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