1 . 有以下命题:设
,
,…
是公差为
的等差数列
中任意
项,若
(
,
,
且
),则
;特别是,当
时,称
为
,
,…
的等差平均项.
(1)已知等差数列
的通项公式为
,根据上述命题,则
,
,
,
的等差平均项为:______ ;
(2)将上述真命题推广到各项为正实数的等比数列中:设
,
,…,
是公比为
的等比数列
中任意
项,若
(
,
,
且
),则______ ;特别是,当
时,称
为
,
,…,
的等比平均项.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/718becd70c94d6876d6e33d6dcd476c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdc291ae9071d0d3ebde20a1cd507577.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ab14f60ca1a64d70a4dd5a662c6530e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72c13c73a017127794debc08dfa029fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de09db4e35fed83c5ac3fb2bbd976906.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8976d0f44ad2fa82e9dae988be07f728.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b427fbf45913f86cc7b4c3bf1749f90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5880f852890d71bb1c95ffe7382e1a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ab1031a0c7db08519d6b56729fc7e2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0116e1383a146ef6406d514764e87666.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de009d9df65374c870a4012cf5db28df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/718becd70c94d6876d6e33d6dcd476c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdc291ae9071d0d3ebde20a1cd507577.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ab14f60ca1a64d70a4dd5a662c6530e.png)
(1)已知等差数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9260f8989cfd0ffca5a49ffbc0668f14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c1ccc6c74b8754e9bcbb3f39a11b6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e35eeaabd951fb09b2926807da3685b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b53c211eecfe7c449b52ace8aef55d58.png)
(2)将上述真命题推广到各项为正实数的等比数列中:设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/718becd70c94d6876d6e33d6dcd476c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdc291ae9071d0d3ebde20a1cd507577.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ab14f60ca1a64d70a4dd5a662c6530e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa8a716a31b0f51b70fdf9bdb257909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4be2164a2c67d6163faee87a10942bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72c13c73a017127794debc08dfa029fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de09db4e35fed83c5ac3fb2bbd976906.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8976d0f44ad2fa82e9dae988be07f728.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b427fbf45913f86cc7b4c3bf1749f90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5880f852890d71bb1c95ffe7382e1a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0116e1383a146ef6406d514764e87666.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de009d9df65374c870a4012cf5db28df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/718becd70c94d6876d6e33d6dcd476c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdc291ae9071d0d3ebde20a1cd507577.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ab14f60ca1a64d70a4dd5a662c6530e.png)
您最近一年使用:0次