Question

1. a class at high school spent the day at an amusement park. in the first hour, they rode 2 rides. after 2 hours, they rode 5 rides. they had ridden 8 rides after 3 hours. create an arithmetic sequence for the nth term of the sequence. find the 10th term of the sequence and interpret the solution in terms of the situation.

Explanation:

Step1: Identify first - term and common difference

The first - term $a_1$ of the arithmetic sequence is the number of rides in the first hour. So, $a_1 = 2$. The common difference $d$ is the increase in the number of rides per hour. Since from 1 hour to 2 hours the number of rides changes from 2 to 5 (an increase of 3), and from 2 hours to 3 hours the number of rides changes from 5 to 8 (also an increase of 3), $d = 3$.

Step2: Find the nth - term formula

The formula for the nth term of an arithmetic sequence is $a_n=a_1+(n - 1)d$. Substituting $a_1 = 2$ and $d = 3$ into the formula, we get $a_n=2+(n - 1)\times3=2 + 3n-3=3n - 1$.

Step3: Find the 10th term

Substitute $n = 10$ into the nth - term formula $a_n=3n - 1$. So, $a_{10}=3\times10 - 1=29$.

Step4: Interpret the 10th term

In the context of the situation, the 10th term represents the number of rides the class will have ridden after 10 hours at the amusement park.

Answer:

The nth - term of the arithmetic sequence is $a_n = 3n - 1$. The 10th term of the sequence is 29, which means that after 10 hours at the amusement park, the class will have ridden 29 rides.