Question

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

Answer 1

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!