document.write( "Question 1110915: the first three terms of an arithmetic projection are x,2x+1 and 5x+1.find x and the sum of the first 10 terms \n" ); document.write( "
Algebra.Com's Answer #725927 by ikleyn(52790)\"\" \"About 
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document.write( "(2x+1) -x = (5x+1) - (2x+1)    (<<<---===  \"a%5B2%5D\" - \"a%5B1%5D\" = \"a%5B3%5D\" - \"a%5B2%5D\")\r\n" );
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document.write( "x + 1 = 3x\r\n" );
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document.write( "1 = 2x  ====>  x = \"1%2F2\" is the first term.\r\n" );
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document.write( "(2x+1) - x = (1+1) - 1/2 = \"3%2F2\" is the common difference.\r\n" );
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document.write( "The 10-th term is   \"1%2F2\" + \"9%2A%283%2F2%29\" = \"%281+%2B+27%29%2F2\" = 14.\r\n" );
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document.write( "The sum of 10 terms = the average of the 1-st and the 10-th terms (which is equal to \"%2814%2B0.5%29%2F2\" = 7.25),  taken 10 times: \r\n" );
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document.write( "Sum = 7.25*10 = 72.5.\r\n" );
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\n" ); document.write( "On arithmetic progressions, see the lessons 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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