Question 1196135
.
After knee surgery, the trainer tells Sarah to return to her jogging program slowly. He
suggests jogging for 12 minutes each day for the first week. Each week thereafter, he
suggests that Sarah increases that time by 6 minutes per day. How many weeks will it
be before she is up to jogging 60 minutes per day?
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<pre>
Arithmetic progression.


First term is 12 (minutes).

Common difference is 6 (minutes).


The question is: what is the number of the term, whose value is 60-6 = 54.


Write the formula for the n-th term of an AP

    {{{a[n]}}} = {{{a[1] + d*(n-1)}}}.


In our case, the formula takes the form

    54 = 12 + 6*(n-1).


From this equation,

    n-1 = {{{(54-12)/6}}} = 7.


Hence, n = 7+1 = 8.    <U>ANSWER</U>


<U>CHECK</U>:         week    the number {{{a[n]}}}

                 1          12
                 2          18
                 3          24
                 4          30
                 5          36
                 6          42
                 7          48
                 8          54    <<<---=== n=8 is the seeking number.
                 9          60              This week (n=9) is with 60 jogging per day, but we look for the week BEFORE it. 

confirming the answer.
</pre>

Solved, checked, and explained.


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For introductory lessons on arithmetic progressions see 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/Arithmetic-progressions.lesson>Arithmetic progressions</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/The-proofs-of-the-formulas-for-arithmetic-progressions.lesson>The proofs of the formulas for arithmetic progressions</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/Problems-on-arithmetic-progressions.lesson>Problems on arithmetic progressions</A>  

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/Word-problems-on-arithmetic-progressions.lesson>Word problems on arithmetic progressions</A>

in this site.


Also, &nbsp;you have this free of charge online textbook in ALGEBRA-II in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-II - YOUR ONLINE TEXTBOOK</A>.


The referred lessons are the part of this online textbook under the topic <U>"Arithmetic progressions"</U>.



Save the link to this textbook together with its description


Free of charge online textbook in ALGEBRA-II
https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson


into your archive and use when it is needed.