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3. or equivalent
Student Lesson Summary
In a geometric sequence, the value of each term is the value of the previous term multiplied by a constant. If you know the constant to multiply by, you can use it to determine the value of other terms. For example, each term in this sequence is 3 times the term before it. (It is usually quicker to say “each term” instead of “the value of each term,” as long as it’s clear what you mean.)
A way to describe this sequence would be: the starting term is 2, and then .
This constant multiplier (the “3” in the example) is often called the sequence’s common ratio. To nd it, you can divide consecutive terms. This can also help you decide whether a sequence is geometric.
For example, consider . If you divide each term by the previous term, you get 0.2 each time: . So, the sequence geometric.
Unit 1
Lesson 2: Introducing Geometric Sequences 25