document.write( "Question 916465: A geometric sequence has a second term of 6 and the sum of the first 3 term is -14. Find its fourth term. \n" ); document.write( "
Algebra.Com's Answer #556133 by Edwin McCravy(20059)\"\" \"About 
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A geometric sequence has a second term of 6:
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document.write( "\"a%5B2%5D=6\"\r\n" );
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document.write( "The first term is the second term divided by the common ratio r.\r\n" );
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document.write( "\"a%5B1%5D=6%2Fr\"\r\n" );
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document.write( "The third term is the second term multiplied by the common ratio r.\r\n" );
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document.write( "\"a%5B3%5D=6r\"\r\n" );
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\n" ); document.write( "and the sum of the first 3 term is -14
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document.write( "\"a%5B1%5D%2Ba%5B2%5D%2Ba%5B3%5D=-14\"\r\n" );
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document.write( "\"6%2Fr%2B6%2B6r=-14\"\r\n" );
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document.write( "Clear the fraction by multiplying through by r\r\n" );
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document.write( "\"6%2B6r%2B6r%5E2=-14r\"\r\n" );
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document.write( "\"6%2B20r%2B6r%5E2=0\"\r\n" );
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document.write( "Divide through by 2\r\n" );
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document.write( "\"3%2B19r%2B3r%5E2=0\"\r\n" );
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document.write( "Arrange in descending order\r\n" );
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document.write( "\"3r%5E2%2B10r%2B3=0\"\r\n" );
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document.write( "Factor:\r\n" );
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document.write( "\"%283r%2B1%29%28r%2B3%29=0\"\r\n" );
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document.write( "Use zero-factor property:\r\n" );
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document.write( "3r+1=0;   r+3=0\r\n" );
document.write( "  3r=-1;    r=-3\r\n" );
document.write( "   r=\"-1%2F3\"\r\n" );
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document.write( "So there will be two solutions to this problem.\r\n" );
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document.write( "Using r=\"-1%2F3\", the sequence is\r\n" );
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document.write( "\"a%5B1%5D=6%2Fr=6%2F%28-1%2F3%29=6%2A%28-3%2F1%29=-18\"\r\n" );
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document.write( "\"a%5B2%5D=6\"\r\n" );
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document.write( "\"a%5B3%5D=6%28-1%2F3%29=-2\"\r\n" );
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document.write( "\"a%5B4%5D=%28-2%29%28-1%2F3%29=2%2F3\"\r\n" );
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document.write( "-18,6,-2,\"2%2F3\"\r\n" );
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document.write( "Fourth term = \"2%2F3\"\r\n" );
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document.write( "Using r = -3, the sequence is\r\n" );
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document.write( "\"a%5B1%5D=6%2Fr=6%2F%28-3%29=-2\"\r\n" );
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document.write( "\"a%5B2%5D=6\"\r\n" );
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document.write( "\"a%5B3%5D=6%28-3%29=-18\"\r\n" );
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document.write( "\"a%5B4%5D=%28-18%29%28-3%29=54\"\r\n" );
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document.write( "-2, 6, -18, 54\r\n" );
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document.write( "Fourth term = 54.\r\n" );
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document.write( "------\r\n" );
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document.write( "Edwin
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