Chapter 2: Introduction to Linear Polynomials
Chapter 2: Introduction to Linear Polynomials
Exercise
Question
Question: 12 (iv)
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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.
(iv) How many matchsticks will be required for the 15th stage of the pattern?
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Answer
1
Recall the expression derived in the previous question for the number of matchsticks in the nth stage.
Matchstick count in the $n$th stage = $6 + 5(n - 1)$
2
Substitute n = 15 into the expression and simplify.
\text{$6 + 5 × ({color:#2E2EFF}15{/color} - 1)$}
⇒
$6 + 5 × 14$
⇒
$6 + 70$
⇒
$76$
3
Write the number of matchsticks required.
Answer: 76 matchsticks