若数列{an}满足:a1=1,an+1=2an(n∈N+),则a5=_.
问题描述:
若数列{an}满足:a1=1,an+1=2an(n∈N+),则a5=______.
答
(法一):∵an+1=2an,a1=1
∴
=2an+1 an
∴数列{an}是以1为首项,以2为公比的等比数列
由等比数列的通项公式可得,an=2n-1
∴a5=24=16
(法二):∵an+1=2an=22an-1=23an-2=…=2na1=2n
∴an=2n-1
a5=24=16
故答案为:16