Final answer:
To determine how many miles Melinda will jog on day 17, one must calculate the 17th term of a geometric progression where the first term is 1.25 miles, and the common ratio is 1.2. The 17th term is found using the formula T_n = a × r^(n-1), which is 1.25 × 1.2^16 for this specific problem.
Step-by-step explanation:
The question deals with a geometric progression in which Melinda increases her jogging distance each day by a constant ratio. Melinda starts jogging on day 1 with a distance of 1 and one fourth miles (which is 1.25 miles). On day 2, she increases her jogging distance by one fifth of day 1, which is ⅔ of 1.25 miles or 0.25 miles. Therefore, on day 2, she jogs a total of 1.5 miles (1.25 + 0.25).
To find out how much she will jog on day 17, we can use the formula for the sum of a geometric series:
S_n = a × [(1 - r^n) / (1 - r)], where:
a is the first term,
r is the common ratio, and
n is the number of terms.
In this case, the first term a = 1.25 and r = 1 + ⅔ = 1.2. We want the 17th term, so n = 17.
To find the 17th term directly, we use the formula for the nth term of a geometric series:
T_n = a × r^(n-1)
T_17 = 1.25 × 1.2^(17-1) = 1.25 × 1.2^16
Melinda will have to do the calculation to determine the exact distance she will jog on day 17.