To train for a race, Will begins by jogging 11 minutes one day per week. He increases his jogging time by 5 minutes each week. Write the general term of this arithmetic sequence, and find how many whole weeks it takes for him to reach a jogging time of one hour

T(min) W(weeks)

11 0
16 1.
21 2.
26 3.
31 4.

Eq: T = 5W + 11.

Example: Let W = 4 weeks.
T = 5*4 + 11 = 31min.

T = 1hr = 60min.
T = 5W + 11 = 60min,
5W + 11 = 60,
5W = 60 - 11 = 49,
W = 49 / 5 = 9.8wks or 9 Whole weeks.

this is all wrong

The general term of an arithmetic sequence can be represented by the equation:

a_n = a_1 + (n-1) * d

where:
a_n is the value of the n-th term,
a_1 is the value of the first term, and
d is the common difference.

In this case:
a_1 = 11 minutes (the starting time),
d = 5 minutes (the increase in jogging time per week),
a_n = 60 minutes (one hour, the target jogging time).

To find the number of weeks it takes for Will to reach a jogging time of one hour, we need to solve the equation:

60 = 11 + (n-1) * 5

Simplifying the equation:
60 = 11 + 5n - 5
60 - 11 + 5 = 5n
54 = 5n

Dividing both sides of the equation by 5:
n = 54 / 5
n ≈ 10.8

Since the number of weeks must be a whole number, it will take approximately 11 weeks for Will to reach a jogging time of one hour.

To find the general term of an arithmetic sequence, we need to identify the first term and the common difference.

In this case, the first term (a₁) is 11 minutes and the common difference (d) is 5 minutes. Each week, Will increases his jogging time by 5 minutes.

The general term (aₙ) of an arithmetic sequence can be calculated using the formula:

aₙ = a₁ + (n - 1) * d

where "aₙ" is the nth term, "a₁" is the first term, "n" is the number of terms, and "d" is the common difference.

Substituting the values we have:

aₙ = 11 + (n - 1) * 5

Now, we want to find how many whole weeks it takes for Will to reach a jogging time of one hour (60 minutes). This can be expressed as finding the value of "n" that makes aₙ equal to 60 minutes.

So we can set up the equation:

60 = 11 + (n - 1) * 5

To solve for "n", let's simplify the equation:

60 = 11 + 5n - 5
49 = 5n - 5
54 = 5n
n = 10.8

Since "n" represents the number of weeks, we can't have a fraction of a week. So we need to round our answer up to the nearest whole week.

Therefore, it takes Will approximately 11 weeks to reach a jogging time of one hour.