Squares Pattern: Number of Squares and Perimeter
Squares Pattern: Number of Squares and Perimeter
TGM Original
Study the sequence of patterns formed by squares and the table below.
| Pattern no. | No. of squares | External perimeter |
|---|---|---|
| \(1\) | \(3\) | \(8\) |
| \(2\) | \(8\) | \(12\) |
| \(3\) | \(15\) | \(16\) |
| \(4\) | \(24\) | \(20\) |
| \(\vdots \) | \(\vdots \) | \(\vdots \) |
| \(8\) | \(p\) | \(q\) |
| \(\vdots \) | \(\vdots \) | \(\vdots \) |
| \(n\) | \({{S}_{n}}\) | \({{P}_{n}}\) |
- 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 \(k\).
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Answer:(a) \(p=80,\ q=36\) (b) \(S_n=(n+1)^2-1,\ P_n=4n+4\) (c) \(k=25\)
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