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. which explicit formula models this situation? a. $a_n = 100 + (n - 1)4$ b. $a_n = 4 + (n - 1)100$ c. $a_n = 100 + (n - 1)21$ d. $a_n = 21 + (n - 1)4$

Explanation:

Step1: Identify the sequence type

This is an arithmetic sequence problem. The explicit formula for an arithmetic sequence is $a_n = a_1 + (n - 1)d$, where $a_1$ is the first term and $d$ is the common difference.

Step2: Determine $a_1$ and $d$

• The first term $a_1$: Marika starts by sprinting 100 yards, so $a_1 = 100$.
• The common difference $d$: She adds 4 yards a day, so $d = 4$.

Step3: Substitute into the formula

Substitute $a_1 = 100$ and $d = 4$ into the arithmetic sequence formula $a_n = a_1 + (n - 1)d$. We get $a_n = 100 + (n - 1)4$.

Answer:

A. $a_n = 100 + (n - 1)4$