document.write( "Question 1052919: Given the arithmetic series 2+4+6...=420 find the term a and the common difference \n" ); document.write( "

Algebra.Com's Answer #668235 by ikleyn(52802) $\"\"$ $\"About$

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\n" ); document.write( "Given the arithmetic series 2+4+6...=420 find the term a and the common difference
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document.write( "1.  The common difference is 2.\r\n" );
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document.write( "2.  To find the number of terms, first cancel the given equality by 2. You will get\r\n" );
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document.write( "    1 + 2 + 3 + . . . +  = 210.\r\n" );
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document.write( "    Or, which is the same,\r\n" );
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document.write( "     = 210,\r\n" );
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document.write( "    n*(n+1) = 420.\r\n" );
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document.write( "    420 decomposes into the product of two consecutive natural integers by an unique way: 420 = 20*21.\r\n" );
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document.write( "Answer.  The common difference is 2.\r\n" );
document.write( "         The number of terms is 20.\r\n" );
document.write( "         The 20-th term is  = 2 + 2*(20-1) = 2 + 38 = 40.\r\n" );
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\n" ); document.write( "\n" ); document.write( "On arithmetic progressions, see the lessons\r
\n" ); document.write( "\n" ); document.write( "My lessons on arithmetic progressions in this site are\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
\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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