数列{an}中相邻两项an,an+1是方程x^2+3nx+bn=0两根,已知a10=-10,则b50等于________,.
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![数列{an}中相邻两项an,an+1是方程x^2+3nx+bn=0两根,已知a10=-10,则b50等于________,.](/uploads/image/z/5557894-70-4.jpg?t=%E6%95%B0%E5%88%97%7Ban%7D%E4%B8%AD%E7%9B%B8%E9%82%BB%E4%B8%A4%E9%A1%B9an%2Can%2B1%E6%98%AF%E6%96%B9%E7%A8%8Bx%5E2%2B3nx%2Bbn%3D0%E4%B8%A4%E6%A0%B9%2C%E5%B7%B2%E7%9F%A5a10%3D-10%2C%E5%88%99b50%E7%AD%89%E4%BA%8E________%2C.)
数列{an}中相邻两项an,an+1是方程x^2+3nx+bn=0两根,已知a10=-10,则b50等于________,.
数列{an}中相邻两项an,an+1是方程x^2+3nx+bn=0两根,已知a10=-10,则b50等于________
,.
数列{an}中相邻两项an,an+1是方程x^2+3nx+bn=0两根,已知a10=-10,则b50等于________,.
An,A(n+1)是方程的根 An+A(n+1)=-3n An×A(n+1)=Bn
A(n+1)+A(n+2)=-3(n+1)
A(n+2)-An=-3(n+1)-(-3n)=-3
{An}奇数项、偶数项分别成等差数列,公差为-3
B50=A50×A51
A50-A10=20(A(n+2)-An)=-60 A50=-70
A10+A11=-3×10=-30 A11=-20
A51-A11=20(A(n+2)-An)=-60 A51=-80
B50=(-70)×(-80)=5600
因为an,an+1是方程x^2+3nx+bn=0两根
故a[n]+a[n+1]=-3n (1)
a[n]*a[n+1]=b[n] (2)
对于(1)式:a[n+2]+a[n+1]=-3n-3
相减得 a[n+2]=a[n]-3
即取出{an}的偶数项得到等差数列{cn},其中c[5]=-10,公差为-3
所以a[50]=c[25]=-...
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因为an,an+1是方程x^2+3nx+bn=0两根
故a[n]+a[n+1]=-3n (1)
a[n]*a[n+1]=b[n] (2)
对于(1)式:a[n+2]+a[n+1]=-3n-3
相减得 a[n+2]=a[n]-3
即取出{an}的偶数项得到等差数列{cn},其中c[5]=-10,公差为-3
所以a[50]=c[25]=-10-20*3=-70 a[51]=-a[50]-3*50=-80
b[50]=a[50]*a[51]=5600
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