设Sn是等差数列an的前n项和,s6/s12=3/10,则s3/s9=¿
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设Sn是等差数列an的前n项和,s6/s12=3/10,则s3/s9=¿
![设Sn是等差数列an的前n项和,s6/s12=3/10,则s3/s9=¿](/uploads/image/z/18640938-66-8.jpg?t=%E8%AE%BESn%E6%98%AF%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97an%E7%9A%84%E5%89%8Dn%E9%A1%B9%E5%92%8C%2Cs6%2Fs12%3D3%2F10%2C%E5%88%99s3%2Fs9%3D%26%23191%3B)
设首项为a1,公差为d
s6/s12=3/10,
s6/s12=(6a1+15d)/(12a1+66d)
=3(2a1+5d)/6(2a1+11d)
=(2a1+5d)/2(2a1+11d)
则(2a1+5d)/2(2a1+11d)=3/10
解得a1=2d
则s3/s9=(3a1+3d)/(9a1+36d)
=(6d+3d)/(18d+36d)
=9/54
=1/6
s6/s12=3/10,
s6/s12=(6a1+15d)/(12a1+66d)
=3(2a1+5d)/6(2a1+11d)
=(2a1+5d)/2(2a1+11d)
则(2a1+5d)/2(2a1+11d)=3/10
解得a1=2d
则s3/s9=(3a1+3d)/(9a1+36d)
=(6d+3d)/(18d+36d)
=9/54
=1/6
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