<PRE><B>Question 1151348</B>
&lt;br&gt;
A table showing the original sequence and the rows of first, second, and third differences:&lt;br&gt;&lt;pre&gt;
-1    4   21   53  103  174  269
    5   17   32  50   71   95
      12   15  18   21   24
         3    3   3    3&lt;br&gt;&lt;/pre&gt;
There is a constant difference of 3 in the row of third differences.  To find the next term in the sequence, place another difference of 3 in the third row and work back up the array:&lt;br&gt;&lt;pre&gt;
-1    4   21   53  103  174  269   391
    5   17   32  50   71   95   122
      12   15  18   21   24   27
         3    3   3    3    3&lt;br&gt;&lt;/pre&gt;
The predicted next term of the sequence is 391.&lt;br&gt;
By the way....  The constant difference in the row of third differences means the sequence is generated by a polynomial of degree 3.  The coefficient of the leading term is the constant difference (3) divided by the factorial of the degree of the polynomial (3!=6).  So the coefficient of the leading term is&lt;br&gt;
{{{(3/(3!)) = 3/6 = (1/2)}}}&lt;br&gt;
and the leading term of the polynomial is then&lt;br&gt;
{{{(1/2)x^3}}}&lt;br&gt;

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