SOLUTION: what will be the next number in the series 1,4,20,168,?

Put them in a column

  1
  4
 20
168

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

  1   3
  4  16 
 20 148
168

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 
  4  16 132
 20 148
168

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  119
  4  16 132
 20 148
168

Now that we have completed the difference table,
write another 119 underneath the last number 119

  1   3  13  119
  4  16 132  119
 20 148
168

Add the 119 and the 132, getting 251, and write that underneath 
the 132


  1   3  13  119
  4  16 132  119
 20 148 251
168

Add the 251 and the 148, getting 399, and write that underneath 
the 148:


  1   3  13  119
  4  16 132  119
 20 148 251
168 399

Finally, add the 399 and the 168, getting 567, and write that underneath 
the 168:


  1   3  13  119
  4  16 132  119
 20 148 251
168 399
567

Answer: fifth term = 567

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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

 =  =  = 567

Edwin