SOLUTION: find the next term 1,7,47,?

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Question 1026557: find the next term 1,7,47,?
Found 3 solutions by rothauserc, Edwin McCravy, Alan3354:
Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
1, 7, 47, ?
:
The next term is 317
:
a(n) = 6*a(n-1) + 5*a(n-2) where a(0)=1 and a(1)=7
:
a(4) = 6*47 + 5*7 = 317
:

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
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

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
A case can be made for many different next terms.