SOLUTION: Use differences to find a pattern in the sequence. -1,-4,-10,-11,-1, 26,76. Assuming that the pattern​ continues, the eighth term should be I cannot figure out how to work t

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Question 1082118: Use differences to find a pattern in the sequence. -1,-4,-10,-11,-1, 26,76. Assuming that the pattern​ continues, the eighth term should be
I cannot figure out how to work this problem. Please help.
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!

-1      -4     -10      -11      -1      26      76      
    -3      -6      -1       10      27      50      
        -3       5       11      17      23      
             8       6        6       6       
                -2        0       0      
                     2        0      
                         -2


Calculate the differences between each pair of elements in the sequence. Then calculate the differences between each pair of differences, and so on until you get a row with more than one element where all of the elements are the same. This only works when you have a convergent sequence. Unfortunately, your given sequence does not converge, hence the differences method is inconclusive.

The only way I know to get the next element in the sequence is to assign a sequential x value to each of the sequence elements forming a set of ordered pairs of the form and then find a polynomial of degree that fits the data. Your next element will be where is the derived polynomial. To do this you either use a graphing app that has a curve fitting utility, or you grind a 7X7 system of linear equations.

My graph program gave me and then calculated

John

My calculator said it, I believe it, that settles it
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