等差数列{an},{bn}的前n项和分别为An,Bn,An/Bn=7n+1/4n+27,a5/b5等于多少
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等差数列{an},{bn}的前n项和分别为An,Bn,An/Bn=7n+1/4n+27,a5/b5等于多少
设等差数列{an}的首项为a1,公差为d1,则有:An=(a1+an)n/2=[a1+a1+(n-1)d1]n/2=(2a1+nd1-d1)n/2=(2a1-d1+nd1)n/2.同理Bn=(2b1-d2+nd2)n/2.所以:An/Bn=(2a1-d1+nd1)/(2b1-d2+bd2)=(7n+1)/(4n+27) 所以:2a1-d1=1,d1=7; 2b1-d2=27,d2=4 所以:a1=4,d1=7,b1=31/2,d2=4.an/bn=[a1+(n-1)d1]/[b1+(n-1)d2]=(14n-6)/(8n+23).所以a5/b5=64/63请采纳回答!
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