<PRE><B>Question 967747</B>
For the given series 
3, 6, 11, 18, 27, 38
first differences between numbers in series
3, 5, 7, 9, 11
second differences from first differences is
2, 2, 2, 2
we have a geometric series of order 2, that is
n^2
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return to original sequence
3 6 11 18 27 38
n^2 terms for nth term are
1 4  9 16 25 36
differences is are
2 2  2  2  2  2
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This must mean that the rule to find any nth term in this sequence is;
n^2 +2
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now we can answer the questions
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1) the next two numbers in the sequence are
7^2 +2 = 51
8^2 +2 = 66
the next two numbers are 49, 66
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2) n^2 + 2
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3) take multiplying two n x n matrices, then
there are n^2 elements in the output matrix, that would require 
n*n^2 = n^3 operations to compute the entire matrix - that is, the 
speed of the most straightforward algorithm is O(n^k), where k = 3.
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