Question

Select the correct answer. Select the function that defines the given sequence: -8, -20, -50, –125, -625,...

A. f(n) = -8 × (-3)^(n – 1)

B. f(n) = -8 × (-3)^(n – 1)

C. f(n) = -8 / (1 – n)

D. f(n) = 5 / (n − 1), for n = 2, 3, 4, ...

Answer 1

None of the answer choices provided correctly describe the sequence given (-8, -20, -50, -125, -625), as the pattern observed does not fit with the functions listed.

Step-by-step explanation:

The sequence given is -8, -20, -50, -125, -625, and we need to select the function that defines this sequence. Let's analyze the pattern of the sequence. Looking at the ratio of each term to the previous term:

• -20 / -8 = 2.5
• -50 / -20 = 2.5
• -125 / -50 = 2.5
• -625 / -125 = 5

The pattern changes on the last term, which suggests the sequence may not adhere to a simple geometric rule throughout. The correct function will need to account for these changes.

Looking at the answer choices, we notice that Options A and B are the same and represent a geometric sequence with a common ratio of -3, which does not fit with our observed pattern.

Option C suggests a reciprocal linear function that would not produce the pattern we have observed.

Option D is a ratio of constants that also does not fit the observed pattern. Thus, given the answer choices, none of these functions correctly represents the sequence provided. There may be an error in the answer choices or in the sequence itself.