Question 1163967
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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.<pre>
−1   3   22   61  125  219   348   original sequence
   4   19   39   64  94   129      first differences
    15    20   25  30   35         second differences
        5    5    5   5            constant third difference<br>
There is the constant difference you need.  Continue that common difference for one more step:<br><pre>
−1   3   22   61  125  219   348
   4   19   39   64  94   129
    15    20   25  30   35
        5    5    5   5    5</pre>
Then work back up the array to find the next term of the sequence.<br><pre>
−1   3   22   61  125  219   348   517
   4   19   39   64  94   129   169
    15    20   25  30   35   40
        5    5    5   5    5</pre>
The next term in the sequence is 517.<br>