document.write( "Question 261707: Finish the following sequence: 5, 9, 21, 57, 165, ____, ____ \n" ); document.write( "
Algebra.Com's Answer #192814 by Edwin McCravy(20059)\"\" \"About 
You can put this solution on YOUR website!
Finish the following sequence: 5, 9, 21, 57, 165, ____, ____
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document.write( "Write the 5 numbers in a row\r\n" );
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document.write( "5     9      21      57     165\r\n" );
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document.write( "Between and underneath each adjacent pair of numbers,\r\n" );
document.write( "write the difference between them, that is, the\r\n" );
document.write( "right one minus the left one.  For instance, below\r\n" );
document.write( "I began by subtracting 9-5 getting 4 and writing 4\r\n" );
document.write( "below and between the 5 and the 9.  Next I subtracted\r\n" );
document.write( "21-9 getting 12, and placed it below and between the\r\n" );
document.write( "9 and the 21, and so on.\r\n" );
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document.write( "5     9      21      57     165\r\n" );
document.write( "   4     12      36     108\r\n" );
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document.write( "Notice that that row is a gemetric sequence,\r\n" );
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document.write( "4x3=12, 12x3=36, and 36x3=108,\r\n" );
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document.write( "so the next two numbers in the second row should be\r\n" );
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document.write( "108x3=324 and 324x3=972\r\n" );
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document.write( "So let's write those two numbers on the second row,\r\n" );
document.write( "in red:\r\n" );
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document.write( "5     9      21      57     165\r\n" );
document.write( "   4     12      36     108      324      972  \r\n" );
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document.write( "Now we work backwards from the second row to the first\r\n" );
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document.write( "Add the 324 to the 165, getting 489, and write it above\r\n" );
document.write( "and between the 324 and 972 and beside the 165.\r\n" );
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document.write( "5     9      21      57     165       489\r\n" );
document.write( "   4     12      36     108      324       972  \r\n" );
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document.write( "Fuinally, add the 972 to the 489, getting 1461, and write it above\r\n" );
document.write( "beside the 489.\r\n" );
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document.write( "5     9      21      57     165       489      1461\r\n" );
document.write( "   4     12      36     108      324       972 \r\n" );
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document.write( "So the next two numbers are 489 and 1461.\r\n" );
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document.write( "Edwin
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