Question

数列{an}中，a1=1，对所有的n≥2，都有a1a2a3......an=n²，则a3+a5等于？

求详解！谢谢~~

Answer 1

a1a2=4,a1a2a3=9,所以a3=9/4，
a1a2a3a4=16,a1a2a3a4a5=25，所以a5=25/16
a3+a5=9/4+25/16=61/16

Answer 2

a1a2...an=n²
a1a2...a(n-1)=(n-1)²
an=n²/(n-1)²
a3+a5=3²/(3-1)²+5²/(5-1)²=9/4+25/16=61/16