设sn是等差数列前n项和,若s3/s6=1/3则s6/s12=?答案是3/10

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设sn是等差数列前n项和,若s3/s6=1/3则s6/s12=?答案是3/10
设sn是等差数列前n项和,若s3/s6=1/3则s6/s12=?
答案是3/10

设sn是等差数列前n项和,若s3/s6=1/3则s6/s12=?答案是3/10
3（a1+a3） 1
----------- = ---
6（a1+a6） 3
所以
a1+a1+2d 2
-------------- = ---
a1+a1+5d 3
解得a1=2d
s6 6（a1+a6） 6（a1+a1+5d） 12a1+30d 54d
---- = -------------- = -------------------- = -------------------- = ------
s12 12（a1+a12） 12（a1+a1+11d） 24a1+132d 180d
3
= -----
10
GOOD LUCK~~~

3/7

Sn=na1+(n(n-1)/2)d
所以S3/S6=(a1+d)/(2a1+5d)=1/3
所以a1=2d
而S6/s12=(2a1+5d)/(4a1+22d)
代入得s6/s12=（4d+5d）/(8d+22d)=9/30=3/10

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