document.write( "Question 1163863: Question: The sum of three numbers in a GP is 14. If the first two terms are each increased by 1 and the third term decreased by 1, the resulting sumber are in ARITHMETIC sequence. Find the Geometric sequence.\r
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\n" ); document.write( " a + ar + ar^2 = 14 (1)
\n" ); document.write( " (a+1), (ar+1), (ar^2 - 1) = AP with sum of 15 (2)
\n" ); document.write( " Since the(2) is an AP:(ar+1) = [(a+1) + (ar^2 - 1)]/ 2
\n" ); document.write( " (ar+1) = [a(1+ar^2)]/2
\n" ); document.write( " 2(ar+1) = a(1+ar^2)\r
\n" ); document.write( "\n" ); document.write( "Am I on the right path or does it need some other approach?
\n" ); document.write( "Than you \n" ); document.write( "

Algebra.Com's Answer #788096 by ikleyn(52793) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "Your first equation is\r\n" );
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document.write( "    a + ar + ar^2 = 14     (1)\r\n" );
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document.write( "Let's will make the second equation.\r\n" );
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document.write( "Since the(2) is an AP :  (ar+1) = [(a+1) + (ar^2 - 1)]/ 2\r\n" );
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document.write( "Simplify it by canceling  \"1\" and \"-1\" inside the  [ . . . ].\r\n" );
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document.write( "    (ar+1) = [a + ar^2]/ 2\r\n" );
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document.write( "     2ar + 2 = a + ar^2\r\n" );
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document.write( "     a - 2ar + ar^2 = 2      (2)\r\n" );
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document.write( "Write equations (1) and (2) together\r\n" );
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document.write( "    a + ar + ar^2 = 14      (1)\r\n" );
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document.write( "    a - 2ar + ar^2 = 2      (2)\r\n" );
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document.write( "Subtract eq(2) from eq(1)\r\n" );
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document.write( "       3ar         = 12\r\n" );
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document.write( "        ar         = 12/3 = 4.    (3)\r\n" );
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document.write( "Now, in equation (1),  replace ar by 4  TWO TIMES,  based on (3).  You will get then\r\n" );
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document.write( "     a + 4 + 4r = 14     \r\n" );
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document.write( "     a + r      = 14-4 = 10.\r\n" );
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document.write( "Now you have two equations\r\n" );
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document.write( "    a + r = 10   \r\n" );
document.write( "and\r\n" );
document.write( "    ar    = 4.\r\n" );
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document.write( "You can solve it via substitution  a = 10 - r\r\n" );
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document.write( "    (10-r)*r = 4\r\n" );
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document.write( "    10r - r^2 = 4\r\n" );
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document.write( "    r^2 - 10r + 4 = 0\r\n" );
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document.write( "and so on . . . \r\n" );
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