Chapter 0.2, Problem 1E

To determine

To calculate:The perimeter of the twelfth figure.

Answer to Problem 1E

The perimeter of the twelfth figure is 28.

Explanation of Solution

Given Information: According to the figure 1 the perimeter = 6

For figure 2 = 8 and for the figure 3 = 10

Since, 6,8,10...........n, it asthmatic progressive series, because the common difference are same.

Perimeter = 6 as per figure 1

For figure 2 = 8 and for figure 3 = 10

Since, 6,8,10...........n, this is aAsthmatic progressive series, because the common differences are the same.

Now, first term (a) $=6$ common difference (d ) $=\text{ figure }1–\text{figure}2=8–6=2$

Formula used:

The n^th term of the Asthmatic progressive is $a_n=a+\left(n-1\right)d$

Have to find the 12^th term = $n_{{}_{12}}=a+\left(12-1\right)d$

Calculation:

  $\begin{array}{l}\Rightarrow n_{12}=6+\left(11\right)\times 2\\ \Rightarrow n_{12}=6+22=28\\ \Rightarrow n_{12}=28\end{array}$