document.write( "Question 389734: write a recursive formula for the sequence 15, 26, 48, 92, 180,... Then find the next term \n" ); document.write( "
Algebra.Com's Answer #276261 by Edwin McCravy(20056)\"\" \"About 
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document.write( "The other tutor found a GENERAL formula, not a RECURSIVE formula.\r\n" );
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document.write( "List those in a column beside the numbers n=1 through n=5\r\n" );
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document.write( "n   an\r\n" );
document.write( "1   15\r\n" );
document.write( "2   26 \r\n" );
document.write( "3   48\r\n" );
document.write( "4   92 \r\n" );
document.write( "5  180\r\n" );
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document.write( "Out beside each number, write the difference between it\r\n" );
document.write( "and the number just below it.\r\n" );
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document.write( "n   an\r\n" );
document.write( "1   15  11\r\n" );
document.write( "2   26  22 \r\n" );
document.write( "3   48  44\r\n" );
document.write( "4   92  88 \r\n" );
document.write( "5  180\r\n" );
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document.write( "Observe that those differences are all multiples of 11\r\n" );
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document.write( "n   an\r\n" );
document.write( "1   15  11 = 1×11 \r\n" );
document.write( "2   26  22 = 2×11\r\n" );
document.write( "3   48  44 = 4×11 \r\n" );
document.write( "4   92  88 = 8×11\r\n" );
document.write( "5  180\r\n" );
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document.write( "Next we observe that the numbers 1,2,4,8 are these powers of 2:\r\n" );
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document.write( "20,21,22,23\r\n" );
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document.write( "n   an\r\n" );
document.write( "1   15  11 = 1×11 = 20×11 \r\n" );
document.write( "2   26  22 = 2×11 = 21×11\r\n" );
document.write( "3   48  44 = 4×11 = 22×11 \r\n" );
document.write( "4   92  88 = 8×11 = 23×11\r\n" );
document.write( "5  180\r\n" );
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document.write( "Finally we observe that the exponents of 2 are 1 less than the\r\n" );
document.write( "values on n in the left-most column, and 1 less than n is n-1.\r\n" );
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document.write( "So we think this way :  To get the next term an+1 from the\r\n" );
document.write( "previous term an we must add 2n-1×11.\r\n" );
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document.write( "So the recursion formula is\r\n" );
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document.write( "a1 = 15, an+1 = an + 2n-1×11\r\n" );
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document.write( "So to get the 6th term, a6, from the 5th term, a5,\r\n" );
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document.write( "we substitute 5 for n in an+1 = an + 2n-1×11\r\n" );
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document.write( "a5+1 = a5 + 25-1×11\r\n" );
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document.write( "a6 = a5 + 24×11\r\n" );
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document.write( "Now we substitute 180 for a5\r\n" );
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document.write( "a6 = 180 + 24×11\r\n" );
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document.write( "a6 = 180 + 16×11\r\n" );
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document.write( "a6 = 180 + 176\r\n" );
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document.write( "a6 = 356\r\n" );
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document.write( "Edwin
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