[大连二模]2024年大连市高三适应性测试数学h试题答案 (更新中)

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[大连二模]2024年大连市高三适应性测试数学h试卷答案

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分析把已知数列递推式变形,可得数列{$\frac{1}{{a}_{n}}$}构成以$\frac{1}{2}$为首项,以2为公差的等差数列,求出等差数列的通项公式后可得数列{an}的通项公式.

解答解:由$\frac{1}{{a}_{n}}$=$\frac{1}{{a}_{n-1}}$+2(n≥2),得$\frac{1}{{a}_{n}}-\frac{1}{{a}_{n-1}}=2(n≥2)$,
又a1=2,∴$\frac{1}{{a}_{1}}=\frac{1}{2}$,
则数列{$\frac{1}{{a}_{n}}$}构成以$\frac{1}{2}$为首项,以2为公差的等差数列,
则$\frac{1}{{a}_{n}}=\frac{1}{2}+2(n-1)=\frac{4n-3}{2}$,
∴${a}_{n}=\frac{2}{4n-3}$.
故答案为:$\frac{2}{4n-3}$.

点评本题考查数列递推式,考查了等差关系的确定,训练了等差数列通项公式的求法,是中档题.

[大连二模]2024年大连市高三适应性测试数学h

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