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0、6、—6、18、—30、66找规律,第十个数是什么,列出式子,谢拉
人气:434 ℃ 时间:2019-10-23 06:02:34
解答
分析:0、6、-6、18、-30、66 每相邻两项之间相减,得 6,-12,24,-48,96 (-1)^0*6,(-1)^1*2*6,(-1)^2*4*6,(-1)^3*8*6,(-1)^4*16*6 (-2)^0*6,(-2)^1*6,(-2)^2*6,(-2)^3*6,(-2)^4*6 (-2)^1*(-3),(-2)^2*(-3),(-2)^3*(-3),(-2)^4*(-3),(-2)^5*(-3) 即a1 = 0,a2 = 6,a3 = -6 ,a4 = 18 ,a5 = -30 ,a6 = 66 a2 - a1 = 6 = (-2)^1*(-3),a3 - a2 = -12 = (-2)^2*(-3),a4 - a3 = 24 = (-2)^3*(-3),a5 - a4 = -48 =(-2)^4*(-3) ,a6 - a5 = 96 =(-2)^5*(-3) 所以an - a(n-1) = (-2)^(n-1)*(-3) ,a1 = 0 ,a2 = 6 ,an = (-2)^(n-1)*(-3) + (-2)^(n-2)*(-3) + ...+ (-2)^[n-(n-1)]*(-3) + 0 = (-3)*(-2)[1-(-2)^(n-1)]/[1-(-2)] = 2 + (-2)^n
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