document.write( "Question 1069082: The 12th term of an arithmetic seqence progression is 5.the 7th term of this progression is 9 more than the 4th term. Determine the sum of 20 terms of this progression \n" ); document.write( "
Algebra.Com's Answer #684333 by ikleyn(52794)\"\" \"About 
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\n" ); document.write( "The 12th term of an arithmetic sequence progression is 5. the 7th term of this progression is 9 more than the 4th term.
\n" ); document.write( "Determine the sum of 20 terms of this progression
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document.write( "\"the 7th term of this progression is 9 more than the 4th term.\" means\r\n" );
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document.write( "\"a%5B7%5D-a%5B4%5D\" = 9.   (1)\r\n" );
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document.write( "But, as you know, \"a%5B7%5D\" = \"a%5B1%5D%2B6d\",  \"a%5B4%5D\" = \"a%5B1%5D%2B3d\", therefore,\r\n" );
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document.write( "\"a%5B7%5D-a%5B4%5D\" = 6d - 3d = 3d = 9.\r\n" );
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document.write( "Hence,  d = 3.\r\n" );
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document.write( "Now you can determine the first term \"a%5B1%5D\"  using the condition\r\n" );
document.write( "\"The 12th term of an arithmetic seqence progression is 5.\".\r\n" );
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document.write( "It gives you an equation\r\n" );
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document.write( "\"a%5B1%5D+%2B+11%2A3\" = 5,\r\n" );
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document.write( "which implies \"a%5B1%5D\" = 5 - 11*3 = 5 - 33 = -28.\r\n" );
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document.write( "Having \"a%5B1%5D\" and d, you can calculate the sum of 20 terms of this progression using the formula \r\n" );
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document.write( "\"S%5B20%5D\" = \"%28a%5B1%5D+%2B+%28%28n-1%29%2Ad%29%2F2%29%2An\" = \"%28-28+%2B+%2819%2A3%29%2F2%29%2A20\" = 10.\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( "    - 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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