Question

a ____ describes the repeated or regular relationship between terms in a sequence.
in ecology, the exponential growth of a species under ideal conditions can be modeled as a ____ sequence.
the ratio between consecutive terms in a geometric sequence is always ____.
savings that increase by a fixed amount each month follow an ____ sequence pattern.

Explanation:

1. A recurrence relation defines the repeated/regular link between terms in a sequence.
2. Exponential growth (constant multiplicative change) matches a geometric sequence, where each term is a multiple of the prior one.
3. By definition, consecutive terms in a geometric sequence have a constant (fixed) ratio.
4. A fixed monthly increase (additive change) follows an arithmetic sequence, where each term increases by a constant difference.

Answer:

1. recurrence relation
2. geometric
3. constant (fixed)
4. arithmetic