document.write( "Question 1070260: An arithmetic and geometric series both have the same first terms,a=9. The fifth term of the arithmetic series is equal to the second term of the geometric series minus 1. The sum of first three terms of the geometric series is equal to the twenty eighth term of the arithmetic series. Find the ratio and common difference for each of the series(if the common difference is a whole number) \n" ); document.write( "

Algebra.Com's Answer #685385 by ikleyn(52799) $\"\"$ $\"About$

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\n" ); document.write( "An arithmetic and geometric series both have the same first terms,a=9. The fifth term of the arithmetic series is equal to
\n" ); document.write( "the second term of the geometric series minus 1. The sum of first three terms of the geometric series is equal to the twenty eighth term
\n" ); document.write( "of the arithmetic series. Find the ratio and common difference for each of the series(if the common difference is a whole number)
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document.write( "9 + 4d = 9r-1,           (1)   (\"The fifth term of the arithmetic series is equal to the second term of the geometric series minus 1\")\r\n" );
document.write( "9*(1+r+r^2) = 9 + 27d.   (2)   (\"The sum of first three terms of the geometric series is equal to the twenty eighth term \r\n" );
document.write( "                                 of the arithmetic series.\")\r\n" );
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document.write( "---->  \r\n" );
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document.write( "4d = 9r - 10 ,           (3)\r\n" );
document.write( "r + r^2 = 3d.            (4)\r\n" );
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document.write( "---->\r\n" );
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document.write( "12d = 27r - 30,          (5)\r\n" );
document.write( "4r + 4r^2 = 12d.         (6)\r\n" );
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document.write( "---->\r\n" );
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document.write( "4r + 4r^2 = 27r - 30  --->  4r^2 - 23r + 30 = 0  --->   =  = .\r\n" );
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document.write( "The only INTEGER root is r =  =  = 2.\r\n" );
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document.write( "Then d =  =  = 2.\r\n" );
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document.write( "Answer.  r = 2.  d = 2.\r\n" );
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