Chapter 4.6, Problem 32E

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 32E

Sequence that represents sum of numbers in each roll is $2,5,7,11$ and sequence is NOT arithmetic sequence

Explanation of Solution

Given: Sum of numbers in each roll:

  

Formula Used:

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

Calculation:

Sum of numbers in each roll:

  

Sequence that represents the sum of numbers in each roll is

  $2,5,7,11$

Let us find the difference between each terms of sequence:

  $\begin{array}{l}5-2=3\\ 7-5=2\\ 11-7=4\end{array}$

Since the difference between each terms is NOT common, thus the sequence is NOT arithmetic sequence

Conclusion:

Hence, Sequence that represents the sum of numbers in each roll is $2,5,7,11$ and sequence is NOT arithmetic sequence