Big Ideas Math Integrated I, 2016
BI
Big Ideas Math Integrated I, 2016 View details
2. Inductive and Deductive Reasoning
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Exercise 42 Page 458

How do arithmetic and geometric sequences progress?

Example Solutions:
1: 14, 12, 1, 2, 4

2: 14, 12, 34, 1, 54

3: 14, 12, 14, 12, 14

Practice makes perfect

Since we only have two terms, we cannot tell how the sequence progress. To do this we need at least three terms. For example, it could be an arithmetic sequence, which means there is a common difference separating consecutive terms. It could also be a geometric sequence, which means a common ratio separates consecutive terms. With this information we can write two different sequences.

The sequence could also just be a repetition of the two given numbers.