68791
AssignmentMultiple Choice

Recognizing Patterns

Question 68791 • GA-Algebra: Concepts and Connections CR

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

Answer
A
2.5, 6.25, 15.625, 39.0625, …
B
2.5, 5, 10, 20
C
–10, –7.5, –5, –2.5, …
D
–10, –25, 62.5, 156.25

Explanation

The formula says to add 2.5 to each term to get the next term, so the sequence must have a constant difference of 2.5. In choice C, −7.5 − (−10) = 2.5, −5 − (−7.5) = 2.5, and −2.5 − (−5) = 2.5. The other choices do not increase by 2.5 each time.

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