**Answer:**

Option C. 3, -2, -7, -12....

**Step-by-step explanation:**

The sequence is defined recursively using the formula f(n+1) = f(n) - 5

We have to identify the sequence generated by this formula.

B). 1, -5, 25, -125.....

f(n+1) = -5 and f(n) = 1

Therefore - 5 = 1 - 5

⇒ -5 ≠ -4

This sequence is not following the formula.

B). 2, 10, 50, 250.........

f(n+1) = 10 and f(n) = 2

Now we use the formula

10 = 2 - 5

10 ≠ -3

This sequence is not following the formula.

C). 3, -2, -7, -12

f(n+1) = -2 and f(n) = 3

We put this value in the formula

-2 = 3 - 5

-2 = -2

Therefore , the sequence is following the formula.

D). 4, 9, 14, 19........

f(n+1) = 9 and f(n) = 4

9 = 4 - 5

9 ≠ -1

Therefore the formula is not applicable to form this sequence.

Option C. is the answer.