document.write( "Question 1162673: If the sum of n terms of two arithmetic progressions is in the ratio (3n+8): (7n+15) find the ratio of their 12th term. \n" ); document.write( "

Algebra.Com's Answer #786757 by ikleyn(52788) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( " The problem's formulation is crystally clear. \r
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\n" ); document.write( "\n" ); document.write( " See my solution below.\r
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document.write( "Let a is the first term and d is the common difference of the first AP.\r\n" );
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document.write( "Let b is the first term and e is the common difference of the second AP.\r\n" );
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document.write( "Then\r\n" );
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document.write( "    ( (n/2)*(2a+(n−1)*d) ) / ( (n/2)*(2b+(n−1)*e) ) = (3n+8)/(7n+15)\r\n" );
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document.write( "or\r\n" );
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document.write( "    (2a+(n−1)*d)/(2b+(n−1)*e) = (3n+8)/(7n+15)\r\n" );
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document.write( "or\r\n" );
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document.write( "    ((2a-d) + nd)/((2b-e)+ed) = (3n+8)/(7n+15).\r\n" );
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document.write( "It means that up to a coefficient of proportionality\r\n" );
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document.write( "    2a−d = 8  and  d = 3,  which implies  2a = 11, d =3,  or  a = 5.5, d = 3\r\n" );
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document.write( "also  \r\n" );
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document.write( "    2b−e = 15  and  e = 7,  which implies  2b = 22, e = 7, or  b = 11, e = 7.\r\n" );
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document.write( "Now  the 12-th terms of the progressions are (up to proportionality)\r\n" );
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document.write( "    5.5 + 11*3 = 38.5  and  11 + 7*11 = 88\r\n" );
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document.write( "and their ratio is\r\n" );
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document.write( "     =  = .    ANSWER\r\n" );
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