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Find the common ratio of a geometric sequence given the middle terms are 56 and 168, respectively.
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Remember, the terms of a geometric sequence are found by multiplying the previous term by some common ratio.
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Alternatively, we can say that some common ratio for the sequence can be found by dividing any term by the term that precedes it.
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Formally, π, the common ratio, is π sub π plus one over π sub π for values of π greater than or equal to one.
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Now, weβre told information about the middle terms of the sequence.
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We donβt know how many terms there are in the sequence.
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But we can define these consecutively as π sub π equals 56 and π sub π plus one equals 168, where π is greater than one and less than π.
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Then, the common ratio is simply found by dividing the term 168 by the term that precedes it, 56.
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And 168 divided by 56 is equal to three.
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So the common ratio of a geometric sequence whose middle terms are 56 and 168 is three.