Question

已知數列{an}滿足a1=1,an=3n-1+an-1(n≥2).

(1)求a2,a3.(2)求通項公式an.

 

Answer 1

(1) a2=4,a3=13 (2) an=(3n-1)

【解析】(1)∵a1=1,an=3n-1+an-1,∴a2=4,a3=13.

(2)an=(an-an-1)+…+(a2-a1)+a1

=3n-1+…+31+1

=(3n-1),

∴an=(3n-1).