Question

Freya is training for a track race. She starts by sprinting 200 yards. She gradually increases her distance, adding 5 yards a day for 21 days.
Which explicit formula models this situation?
A. an = 200 + (n - 1)21
B. an = 200 + (n - 1)5
C. an = 21 + (n - 1)5
D. an=5 + (n—1) 200

Answer 1

To find the correct explicit formula that models Freya's training distance over the 21 days, let's break down the situation.

1. **Initial Distance**: Freya starts by sprinting 200 yards on day 1.
2. **Daily Increase**: She increases her distance by 5 yards each day.

Based on these observations, we can formulate the distance she sprints on day \( n \) (where \( n \) is the number of days) as follows:

- On day 1 (when \( n = 1 \)), she runs \( 200 \) yards.
- On day 2 (when \( n = 2 \)), she runs \( 200 + 5 \) yards.
- On day 3 (when \( n = 3 \)), she runs \( 200 + 2 \times 5 \) yards.
- Continuing this pattern, on day \( n \), she will have run:

\[
a_n = 200 + (n - 1) \times 5
\]

This corresponds to option B:

\[
\text{B. } a_n = 200 + (n - 1)5
\]

So the correct explicit formula for the distance Freya runs on day \( n \) is:

**Answer: B. \( a_n = 200 + (n - 1)5 \)**