Question

如果数列an满足a1,a2/a1,a3/a2,...,an/an-1是首项为1,公比为2的等比数列,则a6=

Answer 1

an/a(n-1)=1×2^(n-1)=2^(n-1)

a(n-1)/a(n-2)=2^(n-2)

…………

a2/a1=2

连乘

an/a1=2×2²×...×2^(n-1)=2^[1+2+...+(n-1)]=2^[n(n-1)/2]

an=a1×2^[n(n-1)/2]=1×2^[n(n-1)/2]=2^[n(n-1)/2]

a6=2^(6×5/2)=2^15=32768