Understanding the Common Ratio in Geometric Sequences in Mathematics

Common Ratio r

In mathematics, the common ratio (represented by the letter “r”) is a term used in geometric sequences

In mathematics, the common ratio (represented by the letter “r”) is a term used in geometric sequences. A geometric sequence is a sequence of numbers where each term is derived by multiplying the previous term by a fixed number, known as the common ratio.

To better understand the common ratio, let’s consider an example. Suppose we have a geometric sequence: 2, 4, 8, 16, 32, …

In this sequence, each term is obtained by multiplying the previous term by the common ratio, which in this case is 2. So, if we take the first term (2) and multiply it by the common ratio (2), we get the second term (4). Similarly, by multiplying the second term (4) by the common ratio (2), we get the third term (8), and so on.

Therefore, the common ratio in this sequence is 2.

In general terms, for a geometric sequence with a first term “a” and a common ratio “r”, the terms of the sequence can be calculated using the formula: an = a * r^(n-1), where “an” represents the nth term of the sequence.

The common ratio is a crucial component in analyzing and understanding geometric sequences. It helps to determine the relationship between consecutive terms and allows us to predict future terms of the sequence.

It is also important to note that the common ratio can be either positive or negative, depending on whether the terms of the geometric sequence increase or decrease.

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