luisa ran 3 miles on the 3rd day of a month and she repeated her run every 4 days for the rest of the month. What equation describes the sequence of days of that month that luisa ran
3,7,11,...
a_n = 4n-1; 1 <= n <= 7 or 8, depending on the month
To describe the sequence of days that Luisa ran, we need to determine the pattern of her runs. Luisa ran 3 miles on the 3rd day of the month and repeated her run every 4 days for the rest of the month.
Let's break down the information:
The first day Luisa ran is on the 3rd day of the month.
She then repeated her run every 4 days.
To find the sequence of days Luisa ran, we can start from the 3rd day and add 4 days repeatedly until the end of the month.
Let's denote "D" as the day Luisa ran, starting with D1 being the 3rd day of the month. We can create an equation to represent this pattern:
D(n) = D(1) + (n - 1) * 4
In the equation above:
- D(n) represents the nth day she ran.
- D(1) is the first day she ran, which is the 3rd day of the month.
- (n - 1) is the number of intervals of 4 days between the first day and the nth day. We subtract 1 because D(1) is already accounted for.
Using this equation, we can find the sequence of days Luisa ran by substituting different values of "n".
For example, to find the days she ran for the first 7 days of the month, we can substitute n = 1, 2, 3, 4, 5, 6, and 7 into the equation:
D(1) = 3 + (1 - 1) * 4 = 3
D(2) = 3 + (2 - 1) * 4 = 7
D(3) = 3 + (3 - 1) * 4 = 11
D(4) = 3 + (4 - 1) * 4 = 15
D(5) = 3 + (5 - 1) * 4 = 19
D(6) = 3 + (6 - 1) * 4 = 23
D(7) = 3 + (7 - 1) * 4 = 27
Therefore, the sequence of days Luisa ran for the first 7 days of the month is 3, 7, 11, 15, 19, 23, and 27.