Which sequence could be partially defined by the recursive formula f (n + 1) = f(n) + 2.5 for n ≥ 1?

2.5, 6.25, 15.625, 39.0625, …
2.5, 5, 10, 20
–10, –7.5, –5, –2.5, …
–10, –25, 62.5, 156.25

Option C: –10, –7.5, –5, –2.5, … is the sequence.

Explanation:

The given recursive formula is for

We need to determine the sequence.

The sequence can be determined by substituting n = 1, 2, 3, 4,....

And

2nd term of the sequence:

Substituting n = 1 in the formula , we get,

Simplifying, we have,

Thus, the 2nd term of the sequence is -7.5

3rd term of the sequence:

Substituting n = 2 in the formula , we get,

Simplifying, we have,

Thus, the 3rd term of the sequence is -5

4th term of the sequence:

Substituting n = 3 in the formula , we get,

Simplifying, we have,

Thus, the 4th term of the sequence is -2.5

Therefore, the sequence is –10, –7.5, –5, –2.5, …

Hence, Option C is the correct answer.