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