Question

Which sequence could be generated using the formula f(n + 1) = f(n) - 5?

1. 1, 5, 25, -125
2. 2, 10, 50, 250
3. -2, -7, 12
4. 4, 9, 14, 19

Answer 1

The sequence that could be generated using the formula f(n + 1) = f(n) - 5 is -2, -7, -12.

Step-by-step explanation:

The given formula f(n + 1) = f(n) - 5 generates a sequence by subtracting 5 from each term to get the next term. Let's check each option to see which sequence can be generated using this formula:

Option 1: Starting with 1, if we subtract 5 each time, we get 1, -4, -9, -14. This is not the correct sequence.

Option 2: Starting with 2, if we subtract 5 each time, we get 2, -3, -8, -13. This is not the correct sequence.

Option 3: Starting with -2, if we subtract 5 each time, we get -2, -7, -12. This is the correct sequence.

Option 4: Starting with 4, if we subtract 5 each time, we get 4, -1, -6, -11. This is not the correct sequence.

Therefore, the sequence that could be generated using the formula f(n + 1) = f(n) - 5 is -2, -7, -12.