document.write( "Question 1200503: A ball starting from rest rolls down an inclined plane and passes over 3 in. during the 1st second, 5 in. during the 2nd second, 7 in. during the 3rd second, etc. In what time from the rest will it cover 120 inches? \n" ); document.write( "

Algebra.Com's Answer #834650 by ikleyn(52800) $\"\"$ $\"About$

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\n" ); document.write( "A ball starting from rest rolls down an inclined plane and passes over
\n" ); document.write( "3 in. during the 1st second, 5 in. during the 2nd second, 7 in. during the 3rd second, etc.
\n" ); document.write( "In what time from the rest will it cover 120 inches?
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document.write( "You have this arithmetic progression\r\n" );
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document.write( "    3, 5, 7, . . . \r\n" );
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document.write( "and they want you determine how many terms are needed to get the sum of 120.\r\n" );
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document.write( "Let's consider the sum of the first n positive odd integer numbers\r\n" );
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document.write( "    1 + 3 + 5 + 7 + . . . + (2n-1).\r\n" );
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document.write( "adding the term \"1\" as a very first term.\r\n" );
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document.write( "It is well known fact that this sum is  .\r\n" );
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document.write( "So, we should find n in a way that \r\n" );
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document.write( "    1 + 3 + 5 + 7 + . . . (2n-1) =  = 120 + 1 = 121.\r\n" );
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document.write( "For it, the value of \"n\" should be  n =  = 11.\r\n" );
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document.write( "So, the arithmetic progression 3, 5, 7, . . . should have 11-1 = 10 terms \r\n" );
document.write( "to have the sum equal to 120.\r\n" );
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document.write( "ANSWER. In 10 minutes.\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
\n" ); document.write( "\n" ); document.write( "    - Problems on arithmetic progressions \r
\n" ); document.write( "\n" ); document.write( "    - Word problems on arithmetic progressions\r
\n" ); document.write( "\n" ); document.write( "in this site.\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
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.\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
\n" ); document.write( "
\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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\n" ); document.write( "\n" ); document.write( "into your archive and use when it is needed.\r
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