SOLUTION: 5 10 3 15 20 13 25 30 __

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Question 952539: 5 10 3 15 20 13 25 30 __
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
952539
Observe that the 
1st, 4th, 7th, ... terms form a arithmetic
sequence 5,15,25,...
2nd, 5th, 8th, ... terms form a arithmetic
sequence 10,20,30,...
So we might assume that the 
3rd, 6th, ... terms form a arithmetic
sequence 3,13,...

5 10  3 15 20 13 25 30
----------------------
5       15       25   
  10       20       30
      3       13

We can extend it:

5 10 3 15 20 13 25 30 23 35 40 33 45 50 43
------------------------------------------------
5      15       25       35       45
  10      20       30       40       50
     3       13       23       33       43

For the nth term we get

a%5Bn%5D=expr%2810%2F3%29n%2B5%2F3, if n mod 3 = 1
a%5Bn%5D=expr%2810%2F3%29n%2B10%2F3, if n mod 3 = 2
a%5Bn%5D=expr%2810%2F3%29n-7, if n mod 3 = 0

After a little more work, we can even get the
general nth term as



Note: We would have a much simpler general nth term 
formula if we would call the 1st term the 0th term 
instead.  If you like I can give you that, and its
derivation.

Edwin