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Ezra is training for a track race. He starts by sprinting 100 yards. He gradually increases his distance, adding 5 yards a day for 21 days.

The explicit formula that models this situation is [tex]a_n=100+(n-1) 5[/tex].

How far does he sprint on day 21?

A. 205 yards
B. 225 yards
C. 100 yards
D. 200 yards

Sagot :

GinnyAnsweridn
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
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