Chapter 4.2, Problem 2LC

To determine

To find: The perimeter of $n$ squares.

Answer to Problem 2LC

  $2+2n$ .

Explanation of Solution

Given information :

Number of squares	perimeter
1	4
2	6

The perimeters are in Arithmetic Progression with first term 4 and common difference 2

Let $p(n)$ denotes perimeter of $n$ squares

Therefore $p(n)=4+(n-1)2$

  $=2+2n$

Therefore

  $p(3)=8$

  $\begin{array}{l}p(4)=10\\ p(10)=22\end{array}$

And for some $x$ , $p(x)=62$

Therefore $2x+2=62$

  $x=30$

Therefore table is

Number of squares	Perimeter
1	4
2	6
3	8
4	10
10	22
30	62
n	$2+2n$