document.write( "Question 1196135: After knee surgery, the trainer tells Sarah to return to her jogging program slowly. He
\n" ); document.write( "suggests jogging for 12 minutes each day for the first week. Each week thereafter, he
\n" ); document.write( "suggests that Sarah increases that time by 6 minutes per day. How many weeks will it
\n" ); document.write( "be before she is up to jogging 60 minutes per day?
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Algebra.Com's Answer #828849 by ikleyn(52790)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "After knee surgery, the trainer tells Sarah to return to her jogging program slowly. He
\n" ); document.write( "suggests jogging for 12 minutes each day for the first week. Each week thereafter, he
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\n" ); document.write( "be before she is up to jogging 60 minutes per day?
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document.write( "Arithmetic progression.\r\n" );
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document.write( "First term is 12 (minutes).\r\n" );
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document.write( "Common difference is 6 (minutes).\r\n" );
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document.write( "The question is: what is the number of the term, whose value is 60-6 = 54.\r\n" );
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document.write( "Write the formula for the n-th term of an AP\r\n" );
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document.write( "    \"a%5Bn%5D\" = \"a%5B1%5D+%2B+d%2A%28n-1%29\".\r\n" );
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document.write( "In our case, the formula takes the form\r\n" );
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document.write( "    54 = 12 + 6*(n-1).\r\n" );
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document.write( "From this equation,\r\n" );
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document.write( "    n-1 = \"%2854-12%29%2F6\" = 7.\r\n" );
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document.write( "Hence, n = 7+1 = 8.    ANSWER\r\n" );
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document.write( "CHECK:         week    the number \"a%5Bn%5D\"\r\n" );
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document.write( "                 1          12\r\n" );
document.write( "                 2          18\r\n" );
document.write( "                 3          24\r\n" );
document.write( "                 4          30\r\n" );
document.write( "                 5          36\r\n" );
document.write( "                 6          42\r\n" );
document.write( "                 7          48\r\n" );
document.write( "                 8          54    <<<---=== n=8 is the seeking number.\r\n" );
document.write( "                 9          60              This week (n=9) is with 60 jogging per day, but we look for the week BEFORE it. \r\n" );
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document.write( "confirming the answer.\r\n" );
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\n" ); document.write( "\n" ); document.write( "For introductory lessons on arithmetic progressions see \r
\n" ); document.write( "\n" ); document.write( "    - Arithmetic progressions\r
\n" ); document.write( "\n" ); document.write( "    - The proofs of the formulas for arithmetic progressions \r
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\n" ); document.write( "\n" ); document.write( "Also,  you have this free of charge online textbook in ALGEBRA-II in this site\r
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\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this online textbook under the topic \"Arithmetic progressions\".\r
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\n" ); document.write( "\n" ); document.write( "Save the link to this textbook together with its description\r
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\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-II
\n" ); document.write( "https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson\r
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