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Answer:
a[n] = n^2 -3n -6
Step-by-step explanation:
First differences are ...
-8 -(-8) = 0
-6 -(-8) = 2
-2 -(-6) = 4
Second differences are ...
2 -0 = 2
4 -2 = 2
Constant second differences indicate a degree 2 (quadratic) sequence.
The general formulation can be written as ...
an = a1 +(n -1)(d1 +(n -2)/2(d2)) . . . . where a1 is the first term; d1 is the first first difference; d2 is the second difference
= -8 +(n -1)(0 +(n -2)/2(2)) = -8 +(n -1)(n -2)
an = n^2 -3n -6 . . . . . formula for the n-th term
