Study the sequence of patterns formed by squares and the table below. Pattern no.No. of squaresExter

Question

Study the sequence of patterns formed by squares and the table below. Pattern no.No. of squaresExternal perimeter $1$$3$$8$ $2$$8$$12$ $3$$15$$16$ $4$$24$$20$ $\vdots $$\vdots $$\vdots $ $8$$p$$q$ $\vdots $$\vdots $$\vdots $ $n$${{S}_{n}}$${{P}_{n}}$ State the values of $p$ and $q$. Express ${{S}_{n}}$ and ${{P}_{n}}$ in terms of $n$. Pattern $k$ has an external perimeter of $104$ units. Find the value of $k$.

Accepted Answer

(a) $p=80,\ q=36$ (b) $S_n=(n+1)^2-1,\ P_n=4n+4$ (c) $k=25$

Pattern no.	No. of squares	External perimeter
\(1\)	\(3\)	\(8\)
\(2\)	\(8\)	\(12\)
\(3\)	\(15\)	\(16\)
\(4\)	\(24\)	\(20\)
\(\vdots \)	\(\vdots \)	\(\vdots \)
\(8\)	\(p\)	\(q\)
\(\vdots \)	\(\vdots \)	\(\vdots \)
\(n\)	\({{S}_{n}}\)	\({{P}_{n}}\)

Squares Pattern: Number of Squares and Perimeter

Squares Pattern: Number of Squares and Perimeter

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