已知f（x）=logax（a＞0，a≠1），设数列f（a1），f（a2），f（a3），…，f（an）…是首项为4，公差为2的等差数列．（I）设a为常数，求证：{an}成等比数列；（II）设bn=anf_刷题宝

题干

已知f（x）=log_ax（a＞0，a≠1），设数列f（a₁），f（a₂），f（a₃），…，f（a_n）…是首项为4，公差为2的等差数列．

（I）设a为常数，求证：{a_n}成等比数列；

（II）设b_n=a_nf（a_n），数列{b_n}前n项和是S_n，当a=2时，求S_n．

上一题下一题 0.0难度选择题更新时间:2018-08-09 02:38:18

答案(点此获取答案解析）

证明：（I）f（a_n）=4+（n﹣1）×2=2n+2，

即log_aa_n=2n+2，可得a_n=a²ⁿ⁺²．

∴ $\frac{a_{n}}{a_{n -}}$

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