Question

a 10th grade class at the local high school spent the day at an amusement park. in the first hour, they rode 3 rides. after 2 hours, they rode 5 rides. they had ridden 7 rides after 3 hours. • create an arithmetic sequence for the nth term of the sequence. • find the 9th term of the sequence and interpret the solution in terms of the situation. show your work or explain how you found your answer. enter your answers and your work or explanation in the space provided.

Explanation:

Step1: Identify first - term and common difference

The number of rides forms a sequence \(3,5,7,\cdots\). The first - term \(a_1 = 3\), and the common difference \(d=5 - 3=2\).

Step2: Write the formula for the nth term of an arithmetic sequence

The formula for the nth term of an arithmetic sequence is \(a_n=a_1+(n - 1)d\). Substituting \(a_1 = 3\) and \(d = 2\) into the formula, we get \(a_n=3+(n - 1)\times2\). Simplify it:
\[

$$\begin{align*} a_n&=3 + 2n-2\\ a_n&=2n + 1 \end{align*}$$

\]

Step3: Find the 9th term of the sequence

Substitute \(n = 9\) into the formula \(a_n=2n + 1\).
\[

$$\begin{align*} a_9&=2\times9+1\\ a_9&=18 + 1\\ a_9&=19 \end{align*}$$

\]

Step4: Interpret the 9th - term

In the context of the situation, \(n\) represents the number of hours spent at the amusement park. When \(n = 9\), \(a_9=19\) means that after 9 hours at the amusement park, the 10th - grade class will have ridden 19 rides.

Answer:

The arithmetic sequence for the nth term is \(a_n = 2n+1\). The 9th term of the sequence is 19, which means that after 9 hours at the amusement park, the 10th - grade class will have ridden 19 rides.