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Chapter 10: Problem 89

What is the common ratio in a geometric sequence?

Short Answer

Expert verified
In a geometric sequence, the common ratio is a fixed, non-zero number found by dividing any term in the sequence (except the first) by the preceding term.

Step by step solution

01

- Definition of a geometric sequence

A geometric sequence, often also called a geometric progression, is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio. For instance, if the initial term of the sequence is \(a\) and the common ratio is denoted by \(r\), then the sequence terms can be denoted by: \(a, ar, ar^2, ar^3\), and so on.
02

- Finding the common ratio

The common ratio in a geometric sequence can easily be found by dividing any term in the sequence (except the first) by the preceding term. In more precise mathematical terms, if a sequence is geometric with terms denoted by \(T1, T2, T3, ... Tn\), then the common ratio (r) can be calculated as follows: \(r = Tn / T(n-1)\). This implies that to find the common ratio, one must take any term in the sequence and divide it by the term before it.

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