Explanation:
An = -2 * An-1
What this means is that you multiply -2 to the term to get the next term.
Since our 1st term (A1) is -2, we have:
A2 = -2 * A1 = -2 * (-2) = 4,
A3 = -2 * A2 = -2 * (4) = -8,
A4 = -2 * A3 = -2 * (-8) = 16,
A5 = -2 * A4 = -2 * (16) = -32,
A6 = -2 * A5 = -2 * (-32) = 64.
Hence our first 6 terms in the GP are
-2, 4, -8, 16, -32 and 64.