Chapter 4.7, Problem 75PPE

(a)

To determine

To find: The next figure of the sequence.

Answer to Problem 75PPE

The following figure will be the next figure.

  

Explanation of Solution

Given information: The following sequence of the figure is given,

  

Calculation: The next figure of the sequence is blue pentagon. It is drawn below.

  

(b)

To determine

To find: The color of ${20}^{th}$ figure of the sequence.

Answer to Problem 75PPE

  ${20}^{th}$ figure will be blue in color.

Explanation of Solution

Given information: The following sequence of the figure is given,

  

Calculation: We can see that every third figure is purple in color. So, ${21}^{st}$ figure will also be purple in color. Therefore, ${20}^{th}$ figure will be blue in color because it is lie just before ${21}^{st}$ figure.

(c)

To determine

To find: The number of sides twenty-third figure have.

Answer to Problem 75PPE

  ${23}^{rd}$ figure will have $10$ sides.

Explanation of Solution

Given information: The following sequence of the figure is given,

  

Calculation: Since the number of sides in each group is $3+\left(n-1\right)$ and ${23}^{rd}$ figure is in the group of $8^{th}$ group of three figures.

Therefore, for $8^{th}$ group,

  $\begin{array}{l}\Rightarrow 3+\left(n-1\right)=3+\left(8-1\right)\left[\because n=8\right]\\ =10\end{array}$