Look at the first three stages of a growing pattern of hexagons made using matchsticks. A new hexagon gets added at every stage which shares a side with the last hexagon of the previous stage. Can 200 matchsticks form a stage in this pattern? Justify.

Using the rule \(T_{n} = 5n + 1\), substituting \(T_{n} = 200\), we get
\(200 = 5n + 1\)
Solving for \(n\):
\(5n = 199\)
⇒ \(n = \frac{199}{5}\)
⇒ \(n = 39.8\)
But stage number must be a whole number. Since \(39.8\) is not a whole number, 200 matchsticks cannot form any stage in this pattern,