Polya Problem Solving

So if I remembered correctly I have to tackle a problem with Polya's problem solving strategy. The problem have chosen is really simple, yet the goal is that I carry out Polya's problem solving strategy, and an easy problem does not stop me from doing that. So the question is: Is every sequence of natural numbers finite and explain?

1. Understand the problem
So to answer the question, I either say yes and prove it, or say no and find an example of an infinite sequence of natural numbers.

2. Make a plan
This is one of those questions that are so obvious that direct reasoning can solve it. So the plan is to use direct reasoning.

3. Carry out the plan
It is less work to try to say no first because providing a counterexample is less work than proving something. So I will start by saying no and I will try to find a counterexample. So I know that there are an infinite number of natural numbers since if n is a natural number then n+1 is also. So the sequence 1, 2, 3, 4... is an infinite sequence of natural numbers for each term n, the next term is n+1.

4. Reflect
Saying no worked pretty well because if I had said yes I would have to deal with a non-working proof then conclude that the answer is no which takes a long time. So in a problem where I have no idea whether the answer is yes or no, I should first try the answer that has less work.