document.write( "Question 1162919: the sum of the first four terms of a linear sequence(A.P)is 26 and that of
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Algebra.Com's Answer #786837 by ikleyn(52788) $\"\"$ $\"About$

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document.write( "The sum of the first 4 terms is   +  +  + .\r\n" );
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document.write( "The sum of the next 4 terms is   +  +  + .\r\n" );
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document.write( "Each difference  ,  ,    and    is equal to 4d,\r\n" );
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document.write( "where d is the common difference of the AP.\r\n" );
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document.write( "Therefore,  4*(4d) = 74 - 26,   or  16d = 48;  hence, d = 48/16 = 3.\r\n" );
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document.write( "Next,  26 = 4a + (1+2+3)d = 4a + 6*3 = 4a + 18,  which implies\r\n" );
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document.write( "       4a = 26 - 18 = 8.\r\n" );
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document.write( "Answer.  The first term of the AP is 8/4 = 2;  the common difference is 3.\r\n" );
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\n" ); document.write( "\n" ); document.write( "The goal of this problem is to teach you manipulate with AP terms quickly and informally.\r
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\n" ); document.write( "\n" ); document.write( "It is a simple problem; so, the method of its solution should be adequately simple.\r
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\n" ); document.write( "\n" ); document.write( "On arithmetic progressions, see the lessons \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
\n" ); document.write( "\n" ); document.write( "    - Calculating partial sums of arithmetic progressions \r
\n" ); document.write( "\n" ); document.write( "    - Finding number of terms of an arithmetic progression \r
\n" ); document.write( "\n" ); document.write( "    - Advanced problems on arithmetic progressions \r
\n" ); document.write( "\n" ); document.write( "    - Problems on arithmetic progressions solved MENTALLY \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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