已知数列an满足a1=1,a3+a7=18,且(an-1)+(an+1)=2an(n>=2)(1)求数列an的通项公式 (2)在平面直角坐标系内,设点P(an+1 /2,n^2+16),n属于N*,试求直线OPn斜率的最小值(O为坐标原点)
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![已知数列an满足a1=1,a3+a7=18,且(an-1)+(an+1)=2an(n>=2)(1)求数列an的通项公式 (2)在平面直角坐标系内,设点P(an+1 /2,n^2+16),n属于N*,试求直线OPn斜率的最小值(O为坐标原点)](/uploads/image/z/3984284-20-4.jpg?t=%E5%B7%B2%E7%9F%A5%E6%95%B0%E5%88%97an%E6%BB%A1%E8%B6%B3a1%3D1%2Ca3%2Ba7%3D18%2C%E4%B8%94%28an-1%29%2B%28an%2B1%29%3D2an%28n%3E%3D2%29%281%29%E6%B1%82%E6%95%B0%E5%88%97an%E7%9A%84%E9%80%9A%E9%A1%B9%E5%85%AC%E5%BC%8F+%282%29%E5%9C%A8%E5%B9%B3%E9%9D%A2%E7%9B%B4%E8%A7%92%E5%9D%90%E6%A0%87%E7%B3%BB%E5%86%85%2C%E8%AE%BE%E7%82%B9P%28an%2B1+%2F2%2Cn%5E2%2B16%29%2Cn%E5%B1%9E%E4%BA%8EN%2A%2C%E8%AF%95%E6%B1%82%E7%9B%B4%E7%BA%BFOPn%E6%96%9C%E7%8E%87%E7%9A%84%E6%9C%80%E5%B0%8F%E5%80%BC%28O%E4%B8%BA%E5%9D%90%E6%A0%87%E5%8E%9F%E7%82%B9%29)
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已知数列an满足a1=1,a3+a7=18,且(an-1)+(an+1)=2an(n>=2)(1)求数列an的通项公式 (2)在平面直角坐标系内,设点P(an+1 /2,n^2+16),n属于N*,试求直线OPn斜率的最小值(O为坐标原点)
已知数列an满足a1=1,a3+a7=18,且(an-1)+(an+1)=2an(n>=2)
(1)求数列an的通项公式 (2)在平面直角坐标系内,设点P(an+1 /2,n^2+16),n属于N*,试求直线OPn斜率的最小值(O为坐标原点)
已知数列an满足a1=1,a3+a7=18,且(an-1)+(an+1)=2an(n>=2)(1)求数列an的通项公式 (2)在平面直角坐标系内,设点P(an+1 /2,n^2+16),n属于N*,试求直线OPn斜率的最小值(O为坐标原点)
(an-1)+(an+1)=2an说明an为等差数列
a1=1,a3+a7=18 1+2d+1+6d=18 d=2
an=a1+(n-1)d=2n-1
直线OPn斜率=(n^2+16)/an+1 /2
=(n^2+16)/[2(n+1)-1]/2
=(2n^2+32)/(2n+1)
=(2n-1)/2 +(63/2)/(2n-1)≥3√7
直线OPn斜率的最小值3√7
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