B 1 = (1, 1), B2 = (3 3,2) gives A 1 = (0, 1), A2 = (1, 2), and the equation solved by two points is known.

Step 2: Solve the general formula of Bn ordinate.

Because A 1, A2, ..., An are all on the straight line y=x+ 1, that is to say, the angle between this line and the horizontal line is 45.

Then the triangle A 1B 1A2, A2B2A3 is an isosceles right triangle, and A 1B 1=B 1A2, then the ordinate of B2 is a2b1+b1. Where a2b 1 = a1b1= b1,so the ordinate of B2 is 2B 1C 1, and so on, we can find that the ordinate bn = 2bn-/.

Step 3: Solve the abscissa

It is easy to see from the figure that the abscissas of B 1 and A2 are the same, that of B2 and A3 are the same, and that of B 1 and A 1 and B2 and A2 are the same, that is to say, the abscissas of Bn and A(n+ 1) are actually the same, and the ordinate of An is also the same. The above results show that the ordinate is 2 (n- 1), which meAns that an is also 2 (n- 1), so it is easy to get that the ordinate of A(n+ 1) is 2 N, which is actually the ordinate of B(n+ 1). A(n+ 1) is on the straight line y=x+ 1, so the abscissa is 2 n- 1.

Then bn = (2 n- 1, 2 (n- 1)). This is a general coordinate formula.