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. How many matchsticks will be required for the \(15^{th}\) stage of the pattern?

SOLUTION

Using the rule \(T_{n} = 5n + 1\), substituting \(n = 15\), we get
\(\begin{aligned} T_{15} &= 5(15) + 1 \\ &= 75 + 1 \\ &= 76\end{aligned}\)

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Final Answer : 76 matchsticks will be required.

Use the rule \(T_{n} = 5n + 1\) to find the number of matchsticks at \(n^{th}\) stage.