document.write( "Question 1163967: Construct a difference table to predict the next term of the sequence.
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Algebra.Com's Answer #788228 by greenestamps(13203) $\"\"$ $\"About$

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\n" ); document.write( "Since the problem tells us to construct a difference table to predict the next term of the sequence, we can assume that in fact the sequence is generated by a polynomial function.

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document.write( "−1   3   22   61  125  219   348   original sequence\r\n" );
document.write( "   4   19   39   64  94   129      first differences\r\n" );
document.write( "    15    20   25  30   35         second differences\r\n" );
document.write( "        5    5    5   5            constant third difference
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document.write( "There is the constant difference you need.  Continue that common difference for one more step:
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document.write( "−1   3   22   61  125  219   348\r\n" );
document.write( "   4   19   39   64  94   129\r\n" );
document.write( "    15    20   25  30   35\r\n" );
document.write( "        5    5    5   5    5

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document.write( "Then work back up the array to find the next term of the sequence.
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document.write( "−1   3   22   61  125  219   348   517\r\n" );
document.write( "   4   19   39   64  94   129   169\r\n" );
document.write( "    15    20   25  30   35   40\r\n" );
document.write( "        5    5    5   5    5

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document.write( "The next term in the sequence is 517.

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