题目

Hallmark arrived in my hometown of Calcutta, India when I was 16. On Valentine’s Day(情人节), I waited in line with many other teenagers just for a chance to get into the store. I remember wishing two things. One of them is that the good-looking boy whom I could see through the store window was picking out a gift for me. Unfortunately, Valentine’s Day passed and I received nothing but a lecture from my father on how Western capitalism(资本主义) was ruining your culture. The next Valentine’s Day, I still didn’t have a boyfriend, but I did receive a greeting card from a secr数列{an}满足an=2an-1+2n+1（n∈N*，n≥2），a3=27．（1）求a1，a2的值；（2）是否存在一个实数t，使得bn=12n（an+t）（n∈N*），且数列{bn}为等差数列？若存在，求出实数t；若不存在，请说明理由；（3）求数列{an}的前n项和Sn．