document.write( "Question 697893: What is the 20th term of the sequence that begins −3, 6, −12, 24…? \n" ); document.write( "
Algebra.Com's Answer #430335 by AnlytcPhil(1806)\"\" \"About 
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−3, 6, −12, 24…? \r
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First we check to see whether it's an arithmetic \r\n" );
document.write( "sequence or a geometric sequence or neither:\r\n" );
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document.write( "Check to see if it's an arithmetic sequence:\r\n" );
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document.write( "2nd term - 1st term = 6 - (-3) = 6+3 = 9\r\n" );
document.write( "3rd term - 2nd term = -12 - 6 = - 18\r\n" );
document.write( "4th term - 3rd term = 24 - (-12) = 24 + 12 = 36\r\n" );
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document.write( "No, because if it were those would all be the same and \r\n" );
document.write( "that would be the common difference d.  So it's not an \r\n" );
document.write( "arithmetic sequence.\r\n" );
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document.write( "Check to see if it's a geometic sequence:\r\n" );
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document.write( "2nd term ÷ 1st term = 6 ÷ (-3) = -2\r\n" );
document.write( "3rd term ÷ 2nd term = -12 ÷ 6 = -2\r\n" );
document.write( "4th term ÷ 3rd term = 24 ÷ (-12) = -2\r\n" );
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document.write( "Yes, it's a geometric sequence because those are all the same,\r\n" );
document.write( "and -2 is the common ratio r.\r\n" );
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document.write( "So we use the formula for the nth term of a geometric sequence,\r\n" );
document.write( "which is:\r\n" );
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document.write( "an = a1r(n-1)\r\n" );
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document.write( "where an is the nth term, so n = 20,\r\n" );
document.write( "a1 is the first term, which is -3, \r\n" );
document.write( "and r is the common ratio, which is -2. \r\n" );
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document.write( "a20 = -3(-2)(20-1)\r\n" );
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document.write( "a20 = -3(-2)19\r\n" );
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document.write( "a20 = -3(-2)19\r\n" );
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document.write( "a20 = -3(-524288)\r\n" );
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document.write( "a20 = 1572864\r\n" );
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document.write( "Checking:\r\n" );
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document.write( "Term        \r\n" );
document.write( "no.          term\r\n" );
document.write( "1             -3\r\n" );
document.write( "2             6\r\n" );
document.write( "3             -12\r\n" );
document.write( "4             24\r\n" );
document.write( "5             -48\r\n" );
document.write( "6             96\r\n" );
document.write( "7             -192\r\n" );
document.write( "8             384\r\n" );
document.write( "9             -768\r\n" );
document.write( "10            1536\r\n" );
document.write( "11            -3072\r\n" );
document.write( "12            6144\r\n" );
document.write( "13            -12288\r\n" );
document.write( "14            24576\r\n" );
document.write( "15            -49152\r\n" );
document.write( "16            98304\r\n" );
document.write( "17            -196608\r\n" );
document.write( "18            393216\r\n" );
document.write( "19            -786432\r\n" );
document.write( "20            1572864\r\n" );
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document.write( "Edwin

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