Aisha is starting a running plan to train for a race. In the first week of her running plan, Aisha will run $6$ miles. The plan calls for Aisha to increase her weekly mileage by $2$ . $5$ miles every week. If Aisha sticks to the plan, how many miles would she be expected to run during her $13^{\text {th }}$ week of the training plan? $\newline$ Answer: $\square$ miles

Full solution

Q. Aisha is starting a running plan to train for a race. In the first week of her running plan, Aisha will run

6

miles. The plan calls for Aisha to increase her weekly mileage by

2

5

miles every week. If Aisha sticks to the plan, how many miles would she be expected to run during her

13^{\text {th }}

week of the training plan?

\newline

Answer:

\square

miles

Start with $6$ miles: Aisha starts with $6$ miles in the first week. Each subsequent week, she adds $2.5$ miles to the previous week's mileage. To find the total mileage for the $13$ th week, we need to calculate the sum of an arithmetic sequence where the first term ( $a_1$ ) is $6$ miles, the common difference ( $d$ ) is $2.5$ miles, and the number of terms ( $n$ ) is $13$ .
Calculate nth term: The formula to find the nth term of an arithmetic sequence is given by: nth term = $a_1 + (n - 1) \cdot d$ . We will use this formula to find the mileage for the $13^{\text{th}}$ week.
Substitute values: Substituting the values into the formula, we get: $13^{\text{th}}$ term $= 6 + (13 - 1) \times 2.5$ . This simplifies to: $13^{\text{th}}$ term $= 6 + 12 \times 2.5$ .
Calculate expression: Calculating the expression, we get: $13^{\text{th}}$ term = $6 + 30 = 36$ miles. Therefore, Aisha is expected to run $36$ miles during her $13^{\text{th}}$ week of the training plan.