中興大學

國中數列1+7+18+34+55... ((20點]





1+7+18+34+55+81......誰可以列出公式呢??謝謝^^



T1 = 1 T2 = 7 = 2 + 5(1) T3 = 18 = 3 + 5(1+2) T4 = 34 = 4 + 5(1+2+3) T5 = 55 = 5 + 5(1+2+3+4) T6 = 81 = 6 + 5(1+2+3+4+5) . . . 所以 T(n) = n + 5[1+2+3+...+(n-1)] = n + 5n(n-1)/2 = n(5n - 3)/2



1+7+18+34+55+81......誰可以列出公式呢??謝謝^^Sol１７１８３４５５８１．．．．６１１１６２１２６．．．．．．５５５５．．．．．．．．[a(n+2)－a(n+1)]－[a(n+1)-a(n)]=5a(n+2)－2a(n+1)+a(n)=5E^2－2E+1=0E=1(重根)設a(n)=p*n^2+q*n+ra(1)=p+q+r=1a(2)=4p+2q+r=7a(3)=9p+3q+r=183p+q=65p+q=112p=5p=5/2q=－3/2r=0a(n)=5n^2/2－3n/2

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