Evaluate $$\sum_{k = -3}^2 k^3$$
If I evaluate it using the expression above by putting the lower and upper limits it produces $-27$ for an answer, but when evaluated using the closed form expression of the geometric sequence where I put first term $a = -27$, $n = 3$ and common ratio $r = 3$, it produces the different result.
I believe my common ratio $r = 3$ is incorrect. Can anyone tell me is $r$ value wrong? If yes, then how to calculate common ratio involving the cube or square etc.
EDIT: Earlier I thought it was geometric sequence, but it is arithmetic sequence so I'm looking for d (common difference).
EDIT I: As @Brian M. Scott pointed out, it is neither an arithmetic sequence nor geometric sequence.