√2,3-√2,2,3,4+√2,( )A.5+2√2 B.6+5√2 C.7+3√2 D.9+6√2

作者: tihaiku 人气: - 评论: 0

问题 √2,3-√2,2,3,4+√2,( )

选项 A.5+2√2 B.6+5√2 C.7+3√2 D.9+6√2

答案 C

解析数列无明显特征，优先考虑做差。做差后得到新数列：3-2√2，√2-1，1，√2+1，（）。递推可得：(3-2√2)+2×(√2-1)=1，(√2-1)+2×1=√2+1，即新数列第一项+第二项的2倍=第三项，故新数列的下一项=1+2×(√2+1)=2√2+3，由此可得所求项=(4+√2)+(2√2+3)=3√2+7。故正确答案为C。

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√2,3-√2,2,3,4+√2,( )A.5+2√2 B.6+5√2 C.7+3√2 D.9+6√2

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