Which function describes the arithmetic sequence shown?

1, - 2, - 5, - 8, - 11, ...

A) ƒ (x) = 3x + 4

B) ƒ (x) = 3x - 4

C) ƒ (x) = - 3x + 4

D) ƒ (x) = - 3x - 4

C) ƒ (x) = - 3x + 4

Step-by-step explanation:

The arithmetic sequence has a general form:

f = a + d (x-1)

Where: a is the first term and d is the common difference

For the given arithmetic sequence:

1, - 2, - 5, - 8, - 11, ...

a = 1

d = - 2 - 1 = - 3

So, f (x) = 1 + (-3) (x-1)

∴ f (x) = 1 - 3x + 3

∴ f (x) = - 3x + 4

The answer is option C) ƒ (x) = - 3x + 4