Question

Freya is training for a track race. She starts by sprinting 200 yards. She gradually increased her distance, adding 5 yards a day for 21 days.

The explicit formula that models this situation is an=200+(n-1)5
How far does she sprint on day 21?

Answer 1

To find out how far Freya sprints on day 21 using the explicit formula given, we can substitute \( n = 21 \) into the formula:

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

Substituting \( n = 21 \):

\[
a_{21} = 200 + (21 - 1) \cdot 5
\]
\[
a_{21} = 200 + (20) \cdot 5
\]
\[
a_{21} = 200 + 100
\]
\[
a_{21} = 300
\]

Thus, Freya sprints **300 yards** on day 21.