To determine how far Ezra sprints on day 21, we will use the explicit formula provided: [tex]\( a_n = 100 + (n - 1) \cdot 5 \)[/tex].
Here, [tex]\( n \)[/tex] represents the day number. We need to find the distance sprinted on day 21, so we set [tex]\( n = 21 \)[/tex].
Following the given formula:
1. Substitute [tex]\( n = 21 \)[/tex] into the formula:
[tex]\[ a_{21} = 100 + (21 - 1) \cdot 5 \][/tex]
2. Simplify the term inside the parentheses:
[tex]\[ 21 - 1 = 20 \][/tex]
3. Multiply the result by 5:
[tex]\[ 20 \cdot 5 = 100 \][/tex]
4. Add this result to the initial value of 100 yards:
[tex]\[ 100 + 100 = 200 \][/tex]
Therefore, the distance Ezra sprints on day 21 is 200 yards.
The correct answer is:
D. 200 yards
