List them in a column

  1
  7
 47

To the right of each, subtract the number
from the one just below it:

  1  6
  7 40
 47

To the right of the 6, do the same, subtract
the 6 from the number just below it 40-6 = 34
write 34 out beside the 6:

  1  6 34
  7 40
 47

Put another 34 under the 34

  1  6 34
  7 40 34
 47

Now we work backwards.  Add the 34 and the 40,
which is just left of it, getting 74.  Put the 
74 underneath the 40, to the right of the 74

  1  6 34
  7 40 34
 47 74

Finally we add the 74 and the 47, getting 121,
Put the 147 underneath the 47

  1  6 34
  7 40 34
 47 74
121

That's the next term, 121.

Edwin