The other tutor thought of an easier pattern than I saw.  I didn't
think of an alternating pattern like that, where you do 1 thing one
time and do another thing the next time.  This one is also correct 
and works.  Actually there are an infinite number of patterns.

Write the numbers in a column:

 1
 4
 9
36
41

Subtract each of the first 4 numbers in that column from the one 
just below it and write the answer to the right of that number:

 1   3
 4   5  
 9  27 
36   5
41

Subtract each of the first 3 numbers in that 2nd column from the one 
just below it and write the answer to the right of that number:

 1   3   2
 4   5  22
 9  27 -22
36   5
41

Subtract each of the first 2 numbers in that 1st column from the one 
just below it and write the answer to the right of that number:

 1   3   2  20 
 4   5  22 -44 
 9  27 -22
36   5
41

Subtract the 20 from the -44 just below it, getting -66 and
writing that beside the 20:

 1   3   2  20 -66 
 4   5  22 -44 
 9  27 -22
36   5
41

Now write another -66 under that one

 1   3   2  20 -66 
 4   5  22 -44 -66
 9  27 -22
36   5
41

Add the bottom -66 to the -44, getting -110 and write that
under the -44

 1   3   2   20 -66 
 4   5  22  -44 -66
 9  27 -22 -110
36   5
41

Add the -110 to the -22, getting -132, and write that
under the -22

 1   3    2   20 -66 
 4   5   22  -44 -66
 9  27  -22 -110
36   5 -132
41

Add the -132 to the 5, getting -127, and write that
under the 5.

  1    3    2   20 -66 
  4    5   22  -44 -66
  9   27  -22 -110
 36    5 -132
 41 -127



Add the -127 to the 41, getting -86 and write that
under the 41

  1    3    2   20 -66 
  4    5   22  -44 -66
  9   27  -22 -110
 36    5 -132
 41 -127
-86


So the 6th term term is -86

Want a general formula?



Edwin