Question

若数列{an}对任意m,n属于正整数满足Am+n=Am+An，且A3=8，则a10=？

Answer 1

Am+n=Am+An
令n=1有
Am+1=Am+A1
数列Am是等差数列，首项是A1,公差是A1，从而
Am=A1+(m-1)A1=nA1
A1=A3/3=8/3
A10=10A1=80/3

Answer 2

A3=A1+A2=a1+a1+a2=a1+a2+a3
a1=a3
A2=A1+A1=2a1=a1+a2
a1=a2
a1=a2=a3=8/3
A4=A3+A1=A3+a1
a4=a1
同理a5=a1 a6=a1``````a10=a1
a10=a1=8/3