Is this a Arithmetic or Geometric series?

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$A_n = n^8+7$

Is the above equation an arithmetic or geometric progression?

I would answer neither, but I'm not to sure.

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You are correct; it is neither.

Observe that $A_1 = 8, A_2 = 263, A_3 = 6568$. $A_2/A_1 \not= A_3/A_2$, so it is not geometric. $A_2-A_1 \not= A_3-A_2$, so it is not arithmetic.