Sticks of equal length are used to make a series of patterns. The first ${3}$ patterns are shown b

Question

Sticks of equal length are used to make a series of patterns. The first ${3}$ patterns are shown below. Pattern${1}$${2}$${3}$ No. of sticks used${4}$${10}$${16}$ Write down the number of sticks needed in the ${4}^{\mathrm{th}}$ pattern. Write down, in terms of ${n}$, the number of sticks (${T_n}$) needed in the ${n}^{\mathrm{th}}$ pattern. Hence, find the number of sticks needed in the ${100}^{\mathrm{th}}$ pattern. Explain why ${301}$ sticks cannot be used to form one of the patterns.

Accepted Answer

(a) $22$ sticks (b) $T_n=6n-2$ (c) $598$ sticks (d) $301$ sticks cannot form a pattern because $6n-2=301$ gives $n=50.5$, not an integer.

Patterns Formed by Sticks

Patterns Formed by Sticks

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