We're using proof by mathematical induction to analyze a sequence an. Statement P(n) is defined based on this sequence. How can we determine the truth of P(n) for all natural numbers n based on its properties?
A. Demonstrate P(n) is true for a single arbitrary natural number n.
B. Assume P(k) is true for some natural number k and show it implies P(k+1).
C. Analyze all possible values of n and verify P(n) for each.
D. Find a counterexample where P(n) is false for a specific natural number n.