Question 1195799
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As the other tutor said, any problem like this is nonsense if you are expected to get the "right" answer.<br>
However, in ANY problem like this, you can get AN answer that is mathematically justifiable by assuming the given sequence is formed by a polynomial equation.  In that case, you can find "A" next number using the method of finite differences.<br>
The given sequence has 5 terms, so there is a unique polynomial of degree 4 that produces the sequence.  And in that polynomial of degree 4, the 4th differences are constant.  (If you know some basic calculus, that is saying that the 4th derivative of a polynomial of degree 4 is a constant.)<br>
Use the method of finite differences to find the constant 4th difference<br><pre>

   1      54      375     1372      3645
       53     321     997      2273
          268     676     1276
              408     600
                  192

The constant 4th difference is 192.  Use that constant difference to build back up the array to find the next number in the sequence.

   1      54      375     1372      3645      7986
       53     321     997      2273      4341
          268     676     1276      2068
              408     600       792
                  192      192
</pre>
The next number in the sequence, assuming a polynomial of degree 4, is 7986.<br>
That is one of the answer choices; so apparently this sequence is a polynomial sequence.<br>
Some of the other sequences at the URL referenced by the other tutor MIGHT be polynomial sequences, but others might not.<br>
In the end, you can NEVER know if any answer you get to a problem like this is the "right" answer.<br>