We appreciate your visit to After hip surgery your physical therapist tells you to slowly return to walking The therapist suggests walking for 5 minutes each day for the first. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
Final answer:
It will take 9 weeks before you are up to 45 minutes of walking per day.
Explanation:
To determine the number of weeks it will take to reach 45 minutes of walking per day, we can set up an arithmetic sequence. The first term of the sequence is 5 minutes, and each subsequent term increases by 5 minutes. We want to find the number of terms in the sequence when the total sum reaches 45 minutes.
To find the number of terms, we can use the formula for the sum of an arithmetic sequence: Sn = (n/2)(2a + (n-1)d), where Sn is the sum of the first n terms, a is the first term, and d is the common difference between terms. In this case, a = 5 and d = 5.
Plugging in the values, we have 45 = (n/2)(2(5) + (n-1)(5)). Simplifying the equation, we get 45 = (n/2)(10 + 5n - 5). Multiplying out, we have 45 = (n/2)(5n + 5).
Now we can solve for n. Dividing both sides of the equation by 5, we get 9 = (n/2)(n + 1). Solving further, we have 18 = n(n + 1). This is a quadratic equation which can be factored as 9(2n + 1) = 0. Since n must be a positive integer, the only solution is n = 9.
It will take 9 weeks before you are up to 45 minutes of walking per day.
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The number of weeks, it will take before it is up to 45 minutes of walking per day is, 9 weeks.
What is an arithmetic sequence?
In the arithmetic sequence the common difference remains constant between any two consecutive terms. In this sequence we can get the next term by adding one fixed value which is known as a common difference. It is also known as arithmetic progression(AP).
Formula for any nth term in AP,
T = a + nd
d = T₂-T₁
Where, a is first term , n is nth term and d is common difference
Given that,
The therapist suggests walking for 5 minutes each day for the first week
Increasing that time by 5 minutes per day each week
Number of weeks will it be before you are up to 45 minutes of walking per day = ?
At the end of first week, he will walk for 5 minute
in the beginning of second he started increasing time 5 minutes per day
So, before he reach up to 45 minutes weeks passed,
Before up to 45 minutes,
number of weeks = ?
45 = 5 + 5n
n = 8
Total number of weeks of walking = 1 + 8
= 9
Hence, the number of weeks is 9
To know more about arithmetic sequence check:
https://brainly.com/question/18109692
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