SOLUTION: 1,4,20,126,?

Put them in a column

  1
  4
 20
126

Subtract each number from the one below it and write it out
to the side in a new column:

  1   3
  4  16 
 20 106
126

In the 2nd column subtract each number from the one below it and 
write it out to the side in a new column:

  1   3  13  77 
  4  16  90
 20 106
126

In the 3rd column subtract each (the only) number from the one below 
it (the only one below it) and  write it out to the side in a new column:

  1   3  13  77
  4  16  90
 20 106
126

Now that we have completed the difference table,
write another 77 underneath the last number 77

  1   3  13  77
  4  16  90  77
 20 106
126

Add the 77 and the 90, getting 167 and write that underneath 
the 90


  1   3  13  77
  4  16  90  77
 20 106 167
126

Add the 167 and the 106, getting 273, and write that underneath 
the 106:


  1   3  13  77
  4  16  90  77
 20 106 251
126 273

Finally, add the 273 and the 126, getting 399, and write that underneath 
the 126:


  1   3  13  77
  4  16  90  77
 20 106 251
126 273
399

Answer: fifth term = 399

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There is a way to get the nth term formula:



Substitute n=1

 =  =  = 1

Substitute n=2


 =  = = 4

Substitute n=3

 =  =  = 20

Substitute n=4


 =  =  = 168

Substitute n=5


 =  =  = 399

Edwin