<PRE><B>Question 1092849</B>
&lt;br&gt;You can NEVER be sure of the right answer to any problem like this, because any next number, or next sequence of 2 or 3 or more numbers, is a valid sequence.&lt;br&gt;
However, in each of these sequences there is a nice pattern which makes it possible to find what is PROBABLY the rule for producing the sequence.&lt;br&gt;
In both of the sequences, look at what you have to add to each term to get the next term.  Then look for a pattern in those numbers that you have to add.&lt;br&gt;
first sequence...&lt;br&gt;
  -5 +  8 =  3
   3 + -5 = -2
  -2 +  3 =  1
   1 + -2 = -1
  -1 +  1 =  0&lt;br&gt;
The sequence of numbers you have to add (the sequence of numbers in the middle column) is
  8, -5, 3, -2, 1, ...&lt;br&gt;
Do you see a pattern there?  (hint: look at the original sequence....)&lt;br&gt;
second sequence...&lt;br&gt;
This one is easy, when you look at it the right way:&lt;br&gt;
   1 +  4 =  5
   5 +  9 = 14
  14 + 16 = 30
  30 + 25 = 55&lt;br&gt;
Do you see the pattern in the numbers in the second column?</PRE>