**Aurora's plan **is an illustration of a **geometric sequence**.

- The
**recursive function **is . - She will complete the
**8th station **in 512 minutes

From the question, we have:

<u>(a) The pattern model</u>

To check if it represents an **arithmetic sequence**, we calculate the **common difference **between the **y-coordinates**

The calculated **differences **are not the same;

This means that, the **model **is not **arithmetic**

To check if it represents a **geometric sequence**, we calculate the **ratio **between the **y-coordinates**

The calculated **ratios **are the same;

This means that, the **model **is **geometric**

<u>(b) The recursive function</u>

The **sequence **is given as:

Where:

Rewrite as:

Substitute in

Express 3 as 4 - 1

Represent 4 as n

Hence, the **recursive sequence **is:

<u>(c) The explicit formula</u>

In (a), we have:

The **nth term **of a **geometric sequence **is:

So, we have:

Express 4 as

Apply law of indices

So, the **time **to **complete **the **8th station **is:

Hence, she will **complete **the **8th station **in **512 minutes**

Read more about **geometric sequence** at:

brainly.com/question/11266123