读图“美国本土农业分布图”，完成下题．

    Hello, everyone! I am your1 today. First, I'd like to 2 you something about London before we3London is a very big city of England. The people here are friendly. They are always 4 to tell visitors something about the city.

    London is a busy place. People_5hard. They are very 6 all the time (一直). London is also a very beautiful city. It has a lot of parks and gardens (花园). When you are in London, you can7the British Museum. It can tell you a lot of 8stories. You may also visit9 place. It is the River Thames. It's long and wide. There are many boats on the river.

    May you have a good10！We will get to London in two hours. Now let's have a guessing game.

已知数列{a_n}前n项和S_n满足S_n+1=a₂S_n+a₁，其中a₂≠0．

（Ⅰ）求证数列{a_n}是首项为1的等比数列；

（Ⅱ）当a₂=2时，是否存在等差数列{b_n}，使得a₁b_n+a₂b_n﹣1+a₃b_n﹣2+…+a_nb₁=2ⁿ⁺¹﹣n﹣2对一切n∈N^*都成立？若存在，求出b_n；若不存在，说明理由．