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] ≠ 0
Hence, the given function DO NOT satisfy the sequence.
2) [tex]f(n) = -n -1 [/tex]
for n = 1, f(0) = -1 -1 = -2 ≠ 0
Hence, 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 = 0
for n = 2 , f(2) = -2(2 -1) = -2 x 1 = -2
for n = 3, f(2) = -2(3 -1) = -2 x 2 = -4 ≠ -8
Hence, the given function DO NOT satisfies the sequence.
