等差数列{an}中公比为3，若a1,a3，a4成等比数列，则a2=？
\u5728\u7b49\u6bd4\u6570\u5217{an}\u4e2d,an>0,q\u22601,\u4e14a2,1/2,a3,a1\u6210\u7b49\u5dee\u6570\u5217\uff0c\u5219\uff08a2+a3\uff09/\uff08a3+a4\uff09=\uff1f\u8bbe\u516c\u6bd4\u4e3aq,\u6240\u4ee5a1=a2/q;a3=a2*q;a4=a2*q*q;
\u539f\u5f0f\u53ef\u5316\u4e3a\uff081+q\uff09/(q+q*q);
\u5728\u7b49\u5dee\u6570\u5217\u4e2d\uff0c\u8bbe\u516c\u5dee\u4e3ab\uff0c\u5219\u6709a2+d=1/2\uff1b=>d=1/2-a2;
a3=a2+2d;a1=a2+3d;\u5373a2+3d=a1+a3;\u5c06d=1/2-a2\u5e26\u5165a2+3d=a1+a3,\u8bbe\u5f97\u5230\u7684\u5f0f\u5b50\u4e3a\uff081\uff09\u5f0f\uff1b\u7531\u7b49\u6bd4\u6570\u5217\u5f97\u5230\u7684\u5173\u7cfba2*a2=a1*a3\u4e3a\uff082\uff09\u5f0f\uff1b
\u5c06a1=a2/q;a3=a2*q\u5e26\u5165\uff081\uff09\uff082\uff09\u4e24\u5f0f\uff1b\u5c06\u5f97\u5230\u5173\u4e8ea2\u4e0eq\u7684\u4e24\u4e2a\u5f0f\u5b50\uff0c\u8054\u7acb\u89e3\u65b9\u7a0b\u7ec4\u53ef\u5f97q\u7684\u503c\uff1b\u5e26\u5165\uff081+q\uff09/(q+q*q)\u5373\u53ef;
\u7b2c\u4e00\u6b21\u56de\u7b54\uff0c\u5b8c\u5168\u624b\u6253\uff0c\u671b\u7ed9\u5206----
\u76f4\u63a5\u8bbe\u9996\u9879a\uff0c\u516c\u5deed,a1=a a3=a+2d a4=a+3d.
\u53c8\u5b83\u4eec\u6210\u7b49\u6bd4\u6570\u5217\uff0c\u90a3\u4e48q=a/(a+2d)=(a+2d)/(a+3d)
\u89e3\u5f97\uff0cd= - a/4
\u6240\u4ee5\uff0cq= -2
则a3=a1+2*3=a1+6
a4=a1+3*3=a1+9
a1,a3,a4成等比数列
则(a3)^2=a1*a4
(a1+6)^2=a1*(a1+9)
a1^2+12a1+36=a1^2+9a1
a1=-12
所以a2=a1+3=-12+3=-9
a1=a2/3 a3=a2*3 a4=a2*9三项分别成等比再利用等比中项公式就可以啦~
绛旓細鍏瘮涓3 S1=a1,S2+a2=a1+a2+a2,S3=a1+a2+a3 S3-S2-a2=S2+a2-S1 鎵浠ュ寲绠寰楀埌2a2=a3-a2(浣犳妸s1,s2,s3鍏ㄩ儴鐢╝1,a2,a3浠ｆ浛锛屽氨鍙互鍖栫畝鍑烘潵浜)3a2=a3 鎵浠3/a2=3 鎵浠ュ叕姣斾负3 璁板緱閲囩撼鎴戠殑鍝!
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