Chapter 4.6, Problem 48E

To determine

whether the areas of the given figures form an arithmetic sequence or not and find the value of $f\left(30\right)$

Answer to Problem 48E

The common difference is not same, so the sequence is not arithmetic.

Explanation of Solution

Given:

  

Calculation:

The first term has four square

So, the area for that is

  $a_1=4{\text{ inch}}^2$

Similarly, for the second term have 9 square

So, the area for second term is

  $\begin{array}{l}{a}_2=9\left(1\right)\\ =9{\text{ inch}}^2\end{array}$

And third term has 25 square

So, the area for the third term is

  $\begin{array}{l}{a}_3=25\left(1\right)\\ =25{\text{ inch}}^2\end{array}$

Now, the common difference d is

  $\begin{array}{l}{a}_3-a_2=25-9\\ =16\end{array}$

And

  $\begin{array}{l}{a}_2-a_1=9-4\\ =5\end{array}$

Conclusion:

Since the common difference is not same, so the sequence is not arithmetic.