Chapter 1.5, Problem 1GP

To determine

Find the perimeter of the twelfth figure.

Answer to Problem 1GP

The perimeter of the twelfth figure is 28.

Explanation of Solution

Given:

The figures below are made with toothpicks. Make a table that relates the perimeter to the figure number. Then find the perimeter of twelfth Figure.

Concept Used:

	Figure 1	Figure 2	Figure 3
Perimeter	6	8	10

The perimeter of the figures is in arithmetic sequence: 6, 8, and 10

The common difference between two consecutive figure is 8 − 6 = 2 toothpicks.

This is an arithmetic sequence.

Calculation:

The nth term formula for Arithmetic sequence: $a_n=a_1+d(n-1)$

The first term $a_1$ is the first figure: 6, we can write $a_1$ = 6 and the common difference d = 2

Let we find the perimeter of the twelfth figure by using the nth term formula:

  $\begin{array}{l}{a}_1=6,d=2,\text{find}{a}_{12}=?\\ a_n=a_1+d(n-1)\\ a_{12}=a_1+d(3-1)=6+2(12-1)=6+22=28\end{array}$

Thus, the perimeter of the twelfth figure is 28.