SOLUTION: I have to find the Recursive Definition for the sequence 0,3,7,12,18... I have tried several different ways of writing the formula but none worked. The closest i got was &#12310

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Question 393978: I have to find the Recursive Definition for the sequence 0,3,7,12,18...
I have tried several different ways of writing the formula but none worked. The closest i got was 〖〖(A〗_(n-1))〗^2 +3.
when inputting this it worked for all A's except A_5 which gave me 19 instead of 18. :( somebody please help.
Please and thank you :)
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
Notice that each difference between two successive terms is 3, 4, 5, 6, ...

We can generate a recursive sequence a%5Bn%5D+=+a%5Bn-1%5D+%2B+n+%2B+C where C is constant. Part of this is a little guess and check...I have found that C = 2.

a%5Bn%5D+=+a%5Bn-1%5D+%2B+n+%2B+2, a%5B1%5D+=+0

We can check by substituting a_2, a_3, and so on.