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230问答网 > 数列{An}是公差为-2的等差数列，若A1+A4+…+A97=50,则A3+A6+A9+…+A99= 详细过程，俺是文科生。

数列{An}是公差为-2的等差数列，若A1+A4+…+A97=50,则A3+A6+A9+…+A99= 详细过程，俺是文科生。

2025-02-11 00:41:17

推荐回答（4个）

回答1：

A3=A2-2=A1-2-2=A1-4:
A6=A4-4
A9=A7-4
.......
A99=A97-4
那么：
一共有99/3=33个
A3+A6+A9+…+A99=(A1-4)+(A4-4)+...+(A97-4)=50-4*33=50-132=-82.

回答2：

A(n+2)=An+2d
所以A3+A6+A9+…+A99=(A1+2d)+(A4+2d)+...+(A97+2d)
=(A1+A4+...+A97)+33*2d
=50+66*(-2)
=-82

回答3：

设公差为d，则A3-A1=2d,A6-A4=2d……A99-A97=2d。则所求=A1＋2d＋A4+2d＋……＋A97＋2d=50+66d=-82

回答4：

A1+A4+…+A97=50
A2+A5+…+A98=50+33d=50-66=-16
A3+A6+A9+…………+A99=-16+33d=-16-66=-82

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