document.write( "Question 1121961: The partial sum in the arithmetic series with first term 17 and a common difference of 3 is 30705. How many terms are there in the series? \n" ); document.write( "

Algebra.Com's Answer #737984 by ikleyn(52793) $\"\"$ $\"About$

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document.write( "Use the formula for the sum of the first n terms of an arithmetic progression\r\n" );
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document.write( " =  = .\r\n" );
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document.write( "Substitute the given data to get\r\n" );
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document.write( "30705 = (17+(n-1)*1.5)*n.\r\n" );
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document.write( "Multiply both sides by 2\r\n" );
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document.write( "61410 = 34n +3n*(n-1).\r\n" );
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document.write( "You get a quadratic equation\r\n" );
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document.write( "3n^2 + 31n - 61410 = 0.\r\n" );
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document.write( "Solve it for n\r\n" );
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document.write( " =  = .\r\n" );
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document.write( "Choose the positive root\r\n" );
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document.write( "n =  = 138.\r\n" );
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document.write( "Answer.  138 terms.\r\n" );
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\n" ); document.write( "\n" ); document.write( "There is a bunch of lessons on arithmetic progressions in this site:\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( "    - Mathematical induction and arithmetic progressions\r
\n" ); document.write( "\n" ); document.write( "    - One characteristic property of arithmetic progressions\r
\n" ); document.write( "\n" ); document.write( "    - Solved problems on 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
\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
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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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\n" ); document.write( "\n" ); document.write( "into your archive and use when it is needed.\r
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