List them in a column:

 73 
298 
475 
544
688

Subtract each number from the number just below it
and write it out to the right in a second column:

 73   225 
298   177
475    69 
544   144
688

Subtract each number from the number just below it
and write it out to the right in a third column:

 73   225   -48     
298   177  -108  
475    69    75
544   144
688

Subtract each number from the number just below it
and write it out to the right in a fourth column:

 73   225   -48  -60   
298   177  -108  183
475    69    75
544   144
688

Subtract that number from the number just below it
and write it out to the right in a fifth column:

 73   225   -48  -60  243  
298   177  -108  183
475    69    75
544   144
688


Now put another 243 under that one on the end,
and now we'll work backwards to the first column.

 73   225   -48  -60   243
298   177  -108  183   243 
475    69    75
544   144
688

Add 243 to the 183 just left of it, getting 426
and write it under the 183

  73   225   -48  -60   243
 298   177  -108  183   243 
 475    69    75  426
 544   144   
 688 

Add the 426 to the 75 just left of it, getting 501,
and write it under the 75

  73   225   -48  -60   243
 298   177  -108  183   243 
 475    69    75  426
 544   144   501
 688 

Add the 501 to the 144 just left of it, getting 645,
and write it under the 144.

  73   225   -48  -60   243
 298   177  -108  183   243 
 475    69    75  426
 544   144   501
 688   645 

Finally add the 645 to the 688 just left of it, getting 1333,
and write it under the 688.

  73   225   -48  -60   243
 298   177  -108  183   243 
 475    69    75  426
 544   144   501
 688   645
1333

The next number is 1333.

Edwin