设{an}是公比大于1的等比数列,若a1+a2+a3=7,且a1+3,3a2,a3+4构成等比数列,求数列{an}的通项公式
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![设{an}是公比大于1的等比数列,若a1+a2+a3=7,且a1+3,3a2,a3+4构成等比数列,求数列{an}的通项公式](/uploads/image/z/5080790-38-0.jpg?t=%E8%AE%BE%7Ban%7D%E6%98%AF%E5%85%AC%E6%AF%94%E5%A4%A7%E4%BA%8E1%E7%9A%84%E7%AD%89%E6%AF%94%E6%95%B0%E5%88%97%2C%E8%8B%A5a1%2Ba2%2Ba3%3D7%2C%E4%B8%94a1%2B3%2C3a2%2Ca3%2B4%E6%9E%84%E6%88%90%E7%AD%89%E6%AF%94%E6%95%B0%E5%88%97%2C%E6%B1%82%E6%95%B0%E5%88%97%7Ban%7D%E7%9A%84%E9%80%9A%E9%A1%B9%E5%85%AC%E5%BC%8F)
设{an}是公比大于1的等比数列,若a1+a2+a3=7,且a1+3,3a2,a3+4构成等比数列,求数列{an}的通项公式
设{an}是公比大于1的等比数列,若a1+a2+a3=7,且a1+3,3a2,a3+4构成等比数列,求数列{an}的通项公式
设{an}是公比大于1的等比数列,若a1+a2+a3=7,且a1+3,3a2,a3+4构成等比数列,求数列{an}的通项公式
好像无实根啊,题错了?
a1+a2+a3=7, \x09a2=7- a1- a3, \x09a22=a12+a32+49+a1a3-7a1-7a3
a1xa3=a22 = a12+a32+49+a1a3-7a1-7a3, \x09a12+a32-7a1-7a3+49=0 ------- ①
(a1+3)(a3+4)=(3a2)2= 9a22=9a1a3,\x098a1a3-4a1=3a3+12,\x09a1(8a3-4)=3a3+12,\x09
a1=(3a3+12)/(8a3-4) ------ ②
a1+a3=x,\x09a1a3=y=a22,\x09a2=7-x, y=a22=x2-14x+49
a12+2a1a3+a32-7a1-7a3+49=2a1a3,\x09(a1+a3)2-7(a1+a3)+49=2a1a3,\x09x2-7x+49=2y
x2-7x+49=2(x2-14x+49)=2x2-28x+98,\x09x2-21x+49=0,\x09x=(21+-7√5)/2
x=(21-7√5)/2 = 2.674
y=[(21-7√5)/2]2-14*(21-7√5)/2+49
=(441-294√5+245)/4-147+49√5+49
=(147-49√5)/2 = 18.716
a1=x-a3=2.674-a3
y=a1a3=a3(2.674-a3)= 18.716
a32-2.674a3+18.716=0 (无实根)
x=(21+7√5)/2 = 18.326
y=[(21+7√5)/2]2-14*(21+7√5)/2+49
=(441+294√5+245)/4-147-49√5+49
=(147+49√5)/2 = 128.284
a1=x-a3=18.326-a3
y=a1a3=a3(18.326-a3)= 128.284
a32-18.326a3+128.284=0 (无实根)