Question

已知数列{an},{bn},满足a1=2,b1=1

Answer 1

解an=3/4a（n-1）+1/4b（n-1）+1(1)

bn=1/4a（n-1）+3/4b（n-1）+1 (2)

(1)+(2)得an+bn=a(n-1)+b(n-1)+2,(n>=2)),所以数列an+bn是以a1+b1=2,公差为2的等差数列

cn=an+bn=2+(n-1)*2=2n