已知等差数列{an}和等比数列{bn}满足:a1+b1=3,a2+b2=7,a3+b3=15,a4+b4=35,则a5+b5=______.-数学

题目简介

已知等差数列{an}和等比数列{bn}满足:a1+b1=3,a2+b2=7,a3+b3=15,a4+b4=35,则a5+b5=______.-数学

题目详情

已知等差数列{an}和等比数列{bn}满足:a1+b1=3,a2+b2=7,a3+b3=15,a4+b4=35,则a5+b5=______.
题型:填空题难度:偏易来源:不详

答案

∵a1+b1=3,①
a2+b2=a1+d+b1q=7,②
a3+b3=a1+2d+b1q2=15,③
a4+b4=a1+3d+b1q3=35④
②-①可得,4-d=b1(q-1)
③-②可得,8-d=b1q(q-1)
④-③可得,20-d=b1q2(q-1)
class="stub"4-d
8-d
=class="stub"1
q
class="stub"8-d
20-d
=class="stub"1
q

class="stub"4-d
8-d
=class="stub"8-d
20-d

解方程可求d=2,q=3,b1=1,a1=2
∴a5+b5=10+81=91
故答案为:91

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