Question

A sequence is defined recursively using the formula f(n + 1) = f(n) – 5 . Which sequence could be generated using this formula?

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

Answer 1

The recurrence f(n+1)=f(n)−5 means each term is 5 less than the previous (common difference −5). Only sequence 3 has that:

3, −2, −7, −12, ... (each step subtracts 5).