document.write( "Question 1199651: The sum of the first four terms of a linear sequence A.p is 26 and that of the next four term is 74. find the value of the first term ,the common difference \n" ); document.write( "

Algebra.Com's Answer #833608 by ikleyn(52790) $\"\"$ $\"About$

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\n" ); document.write( "The sum of the first four terms of a linear sequence A.p is 26
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\n" ); document.write( "find the value of the first term ,the common difference
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document.write( "We are given\r\n" );
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document.write( "     +  +  +  = 26,    (1)\r\n" );
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document.write( "     +  +  +  = 74.    (2)\r\n" );
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document.write( "It is the same as\r\n" );
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document.write( "     + (1+2+3)d   = 26,     \r\n" );
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document.write( "     + (4+5+6+7)d = 74,\r\n" );
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document.write( "or\r\n" );
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document.write( "     +  6d = 26,   (3)\r\n" );
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document.write( "     + 22d = 74.   (4)\r\n" );
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document.write( "From (4), subtract (3).  You will get\r\n" );
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document.write( "    22d - 6d = 74 - 26 \r\n" );
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document.write( "       16d   =    48\r\n" );
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document.write( "         d   =    48/16 = 3.\r\n" );
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document.write( "Thus the common difference of this AP is 3.\r\n" );
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document.write( "Next, from (3)\r\n" );
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document.write( "     = 26 - 6*3 = 26 - 18 = 8,\r\n" );
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document.write( "     = 8/4 = 2.\r\n" );
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document.write( "ANSWER.  The first term of the AP is 2;  the common difference is 3.\r\n" );
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document.write( "CHECK.  Use equation (4) to check this answer ON YOUR OWN.\r\n" );
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