Answer:None of the given functions can be used to define this sequence.Step-by-step explanation:Here the given sequence is 0, -2, -8 , -18 , -32, ....The given function are [tex]f(n) = -2n^{2} , f(n) = -n -1 , f(n) = -2(n-1)[/tex]Now, check for each functions: 1) [tex]f(n) = -2n^{2}[/tex]for n = 1 , [tex]f(1) = -2(1)^{2} = -2[/tex] ≠ 0Hence, the given function DO NOT satisfy the sequence.2) [tex]f(n) = -n -1 [/tex]for n = 1, f(0) = -1 -1 = -2 ≠ 0Hence, the given function DO NOT satisfies the sequence.3) [tex]f(n) = -2(n -1) [/tex]for n = 1 , f(1) = -2(1 -1) = -2 x 0 = 0for n = 2 , f(2) = -2(2 -1) = -2 x 1 = -2for n = 3, f(2) = -2(3 -1) = -2 x 2 = -4 ≠ -8Hence, the given function DO NOT satisfies the sequence.