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^("th ") week of the training plan? Answer: □ miles

Question

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^("th ") week of the training plan? Answer: □ miles

Bytelearn · Accepted Answer

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 13th week, we need to calculate the sum of an arithmetic sequence where the first term (a1) 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 = a1 + (n - 1) * d. We will use this formula to find the mileage for the 13th week.Substitute values: Substituting the values into the formula, we get: 13th term = 6 + (13 - 1) * 2.5. This simplifies to: 13th term = 6 + 12 * 2.5.Calculate expression: Calculating the expression, we get: 13th term = 6 + 30 = 36 miles. Therefore, Aisha is expected to run 36 miles during her 13th week of the training plan.

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