Chapter 11.1, Problem 5WE

To determine

To calculate:

The following sequence is arithmetic, geometric or neither and the missing terms:

  $18,22,26,?,34,?$

Answer to Problem 5WE

The sequence is arithmetic sequence and the missing terms are $30$ and $38$ .

Explanation of Solution

Given information:

  $18,22,26,?,34,?$

Calculation:

Check the common difference first to categorize the given sequence into arithmetic, geometric or neither:

  $\begin{array}{l}{a}_1=18\\ a_2=22\\ a_3=26\\ a_4=?\\ a_5=34\\ a_6=?\end{array}$

Now, the common difference is calculated as:

  $\begin{array}{l}r=a_2-a_1=22-18=4\\ r=a_3-a_2=26-22=4\end{array}$

Therefore, the given sequence is arithmetic sequence.

Now, the missing terms are calculated as:

  $\begin{array}{l}{a}_4=a+\left(n-1\right)r=18+\left(4-1\right)\left(4\right)=18+12=30\\ a_6=a+\left(n-1\right)r=5+\left(6-1\right)\left(4\right)=18+20=38\end{array}$