Question

Marika is training for a track race. She starts by sprinting 100 yards. She gradually increases her distance, adding 4 yards a day for 21 days.
The explicit formula that models this situation is an = 100 + (n - 1)4.
How far does she sprint on day 21?
A. 184 yards
B. 221 yards
C. 200 yards
D. 180 yards

Answer 1

To find out how far Marika sprints on day 21 using the explicit formula \( a_n = 100 + (n - 1) \cdot 4 \), we need to substitute \( n \) with 21.

So the calculation is:

\[
a_{21} = 100 + (21 - 1) \cdot 4
\]

Calculating it step-by-step:

1. Calculate \( 21 - 1 \):
\[
21 - 1 = 20
\]

2. Multiply the result by 4:
\[
20 \cdot 4 = 80
\]

3. Add this to 100:
\[
100 + 80 = 180
\]

Thus, on day 21, Marika sprints **180 yards**.

The answer is **D. 180 yards**.