Question 1164340
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Although there is an apparent mathematical pattern to the given numbers, the question is actually invalid.  ANY next number would make a valid sequence.<br>
ANY problem like this, in which there is no mention of what kind of sequence it is, is invalid for the same reason.<br>
Nevertheless, we can assume that the problem is supposed to be solved using the apparent pattern....<br>
Here is a way to show the process of finding the next number that does exactly the same thing as shown by the other tutor, but in a different way.<br><pre>
1   6  15  28  45  (given sequence)
  5   9  13  17    (first differences -- differences between terms of given sequence)
    4   4   4       (second differences -- differences between successive first differences)</pre>
The constant second differences tell us that the sequence is produced by a polynomial of degree 2.  We could go ahead and find that polynomial if we wanted.<br>
But to find the next number in the sequence, we only need to continue the pattern of constant second differences and then work back up the array.<br><pre>
1   6  15  28  45  66
  5   9  13  17  21
    4   4   4   4</pre>
ANSWER: The next number in the sequence (ASSUMING A SEQUENCE GENERATED BY A POLYNOMIAL) is 66.<br>