Big Ideas Math Integrated I, 2016
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Big Ideas Math Integrated I, 2016 View details
5. Geometric Sequences
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Exercise 49 Page 312

Two terms are dependent if one can be obtained from the other following a specific rule. On the other hand, two terms are independent when they are not related at all.

Dependent, see solution.

Practice makes perfect
Let's start by clarifying what we mean by dependent and independent terms. Two terms are dependent if one can be obtained from the other following a specific rule. On the other hand, two terms are independent when they are not related at all. Now, consider the geometric sequence shown below.
geometric sequence

The sequence above has a common ratio of 2, and therefore the next term can always be obtained from its previous term by multiplying by 2. Note that we can do the same for all geometric sequences by using their corresponding common ratios. Therefore, their terms are dependent.