document.write( "Question 1197283: Find the first term of an Arithmetic sequence , whose 3rd term is 20 and its 6th term is - 4 . \n" ); document.write( "
Algebra.Com's Answer #830499 by ikleyn(52793)\"\" \"About 
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\n" ); document.write( "Find the first term of an Arithmetic sequence , whose 3rd term is 20 and its 6th term is - 4.
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document.write( "Between the 3rd term and 6th term, there are 3 gaps of equal size on the number line.\r\n" );
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document.write( "The size of each gap is  \"%2820+-+%28-4%29%29%2F3\" = \"24%2F3\" = 8 units.\r\n" );
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document.write( "Hence, the common difference of this arithmetic sequence is d = -8 \r\n" );
document.write( "    (it is exactly the gap size, but the sequence is decreasing, so the common difference is negative).\r\n" );
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document.write( "Next, the 1st term is 2 gaps backward from the 3rd term,\r\n" );
document.write( "so, the 1st term is  \"a%5B1%5D\" = 20 - 2*(-8) = 20 + 16 = 36.\r\n" );
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document.write( "ANSWER.  First term of this arithmetic progression is 36.\r\n" );
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document.write( "CHECK.  \"a%5B6%5D\" = \"a%5B1%5D+%2B+5%2Ad\" = 36 + 5*(-8) = 36 - 40 = -4.   ! correct !\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
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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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