(1)数列{an}满足an+1-an=2,a1=2,求数列{an}的通项公式. (2)设数列{an}满足a1+3a2+32a3+…+3n-1an=n/3,a∈N*.求数列{an}的通项.

问题描述:

(1)数列{an}满足an+1-an=2,a1=2,求数列{an}的通项公式.
(2)设数列{an}满足a1+3a2+32a3+…+3n-1an=

n
3
,a∈N*.求数列{an}的通项.

(1)∵an+1-an=2,a1=2,∴数列{an}为等差数列,∴an=2+(n-1)2=2n.(5分)(2)∵a1+3a2+32a3+…3n−1an=n3,①∴a1+3a2+32a3+…+3n-2an-1=n−13,(n≥2)②①-②,得:3n−1an=n3−n−13=13(n≥2).an=13n...