数学数列题及答案 已知数列【an】各项排成如图所示的三角形阵，数阵中每一行每一个数a1,a2,a4,a7…构成等

\uff082013?\u6f4d\u574a\u4e00\u6a21\uff09\u5df2\u77e5\u6570\u5217{an}\u7684\u5404\u9879\u6392\u6210\u5982\u56fe\u6240\u793a\u7684\u4e09\u89d2\u5f62\u6570\u9635\uff0c\u6570\u9635\u4e2d\u6bcf\u4e00\u884c\u7684\u7b2c\u4e00\u4e2a\u6570a1\uff0ca2\uff0ca4\uff0ca7

\uff08 I \uff09\u2235{bn}\u4e3a\u7b49\u5dee\u6570\u5217\uff0c\u8bbe\u516c\u5dee\u4e3ad\uff0cb1=1\uff0cS5=15\uff0c\u2234S5=5+10d=15\uff0cd=1\uff0c\u2234bn=1+\uff08n-1\uff09\u00d71=n\u20262\u5206\u8bbe\u4ece\u7b2c\u4e09\u884c\u8d77\u6bcf\u884c\u7684\u516c\u6bd4\u90fd\u662fq\uff0c\u4e14q\uff1e0\uff0ca9=b4q2=4q2=16\uff0c\u6545q=2\u20264\u5206\u22341+2+3+\u2026+9=45\uff0c\u6545a50\u662f\u6570\u9635\u4e2d\u7b2c10\u884c\u7b2c5\u4e2a\u6570\uff0c\u800ca50=b10q4=10\u00d724=160\u20267\u5206\uff08\u2161\uff09\u2235Sn=1+2+\u2026+n=n(n+1)2\u20268\u5206\u2234Tn=1Sn+1+1Sn+2+\u2026+1S2n=2(n+1)(n+2)+2(n+2)(n+3)+\u2026+22n(2n+1)=2\uff081n+1-1n+2+1n+2-1n+3+\u2026+12n-12n+1\uff09=2\uff081n+1-12n+1\uff09=2n(n+1)(2n+1)\u202612\u5206

\u8bbe\u8be5\u7b49\u5dee\u6570\u5217\u7684\u516c\u5dee\u4e3ad.
\u56e0\u4e3a\u5728\u7b49\u5dee\u6570\u5217\u4e2d\u6709 a1+a4+a7=3a4=15, \u6240\u4ee5 a4=5.
\u53c8\u56e0\u4e3a a2=a4-2d,a6=a4+2d, \u6240\u4ee5 (a4-2d)*a4*(a4+2d)=45, \u5373
(5-2d)*5*(5+2d)=45, \u7531\u6b64\u53ef\u4ee5\u89e3\u51fa d=2 \u6216\u8005 d=-2.
\u82e5d=2,\u5219\u7531 a1=a4-3d=-1 \u53ef\u77e5\u6b64\u65f6\u7684\u901a\u9879\u516c\u5f0f\u4e3a an=a1+(n-1)d=2n-3;
\u82e5d=-2,\u5219\u7531 a1=a4-3d=11 \u53ef\u77e5\u6b64\u65f6\u7684\u901a\u9879\u516c\u5f0f\u4e3a an=a1+(n-1)d=13-2n.

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