In middle school mathematics, the special value method has a wide range of uses, especially in exams. Using the special value method correctly can save a lot of time. (But not every problem can be solved by the special value method. )

Personally, I think it is easiest to use the special value method, as you wrote. A2=3, a3=2, so the arithmetic difference is-1, then a(3+2)=a5=0, and the answer comes out in a flash.

Let's talk about the general method first. To solve this kind of problems, if you master the nature of arithmetic geometric progression skillfully, you can also use the general method and the special value method at the same speed. In arithmetic progression, the difference between item m (m≥ 1) and item n (n≥ 1) must be (m-n)d(d is the tolerance, regardless of who is bigger or smaller). In this problem, it can be seen as: as-ar=r-s (known conditional substitution) =(s-r)d, so d=- 1. Then according to the above properties, a(s+r)-as=a(s+r)-r=(s+r-s)d=rd, so a(s+r)=rd+r=r(d+ 1)=0.

Having said that, in any case, it is very important to be familiar with knowledge if you want to do this kind of problem well. If you can think of and use flexibility, this problem can be easily solved. Come on!