Elia is training for her first marathon. She currently runs 10 mi. per week, and wants to increase her mileage by 2 mi. every week. If Elia keeps to her training schedule, write a formula to define the number of miles she runs each week.

Question

(1 point)
Responses

a subscript n baseline equals 2 n plus 8
Image with alt text: a subscript n baseline equals 2 n plus 8

a subscript n baseline equals negative 2 n plus 2
Image with alt text: a subscript n baseline equals negative 2 n plus 2

a subscript n baseline equals 2 n plus 10
Image with alt text: a subscript n baseline equals 2 n plus 10

a subscript n baseline equals negative 2 n plus 12

Answer 1

To create a formula that defines the number of miles Elia runs each week, we start with the following information:

• Elia currently runs 10 miles in her first week (when \( n = 0 \)).
• She increases her mileage by 2 miles each subsequent week.

We can represent the miles she runs in week \( n \) with the formula: \[ a_n = 10 + 2n \] where:

• \( a_n \) is the number of miles run in week \( n \),
• 10 is the initial mileage (for \( n = 0 \)),
• \( 2n \) represents the additional miles she runs each week.

Now looking at the response options:

1. \( a_n = 2n + 8 \)
2. \( a_n = -2n + 2 \)
3. \( a_n = 2n + 10 \)
4. \( a_n = -2n + 12 \)

The correct formula is: \[ a_n = 2n + 10 \]

So the answer is: \( a_n = 2n + 10 \).