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Use differences to find a pattern in the sequence.

 

-2, -2, -3, 0, 12, 38, 83 = 

 

Assuming that the pattern continues, the eighth term should be =

 Sep 6, 2017
 #1
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-2, -2, -3, 0, 12, 38, 83.....

Look at the difference between the terms at several levels as follows:
0, -1, 3, 12, 26, 45..............First difference
-1, 4, 9,  14, 19....................Second difference
5, 5, 5, 5.............................Third difference

Now, to get the next term in your sequence, just add the last terms as follows:

5 + 19 + 45 + 83 =152, 5 + 24 + 69 +152 =250.........etc. So, your sequence  would be:

-2, -2, -3, 0, 12, 38, 83, 152, 250, 382........etc.

P.S. You could also use this formula to generate any term that you want:

 a(n) = 1/6 (5n^3 - 33n^2 + 64n - 48) 

 Sep 7, 2017

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