Chapter 4.6, Problem 31E

To determine

To calculate: To write a sequence that represents the number of smileys faces in each group and to find if the sequence is arithmetic

Answer to Problem 31E

Sequence that represents the number of smileys in each group is $4,6,8,10$ and sequence is arithmetic sequence

Explanation of Solution

Given: Number of smiley faces in each group is

  

Formula Used:

Sequence in which difference between the terms is common is referred to as arithmetic sequence.

Calculation:

Sequence that represents the number of smileys in each group is

  $4,6,8,10$

Let us find the difference between each terms of sequence:

  $\begin{array}{l}6-4=2\\ 8-6=2\\ 10-8=2\end{array}$

Since the difference between each terms is common, thus the sequence is arithmetic sequence

Common difference is $-6$

Conclusion:

Hence, Sequence that represents the number of smileys in each group is $4,6,8,10$ and sequence is arithmetic sequence