Common Ratio r
In mathematics, the term “common ratio” is often used in the context of geometric sequences or geometric progressions
In mathematics, the term “common ratio” is often used in the context of geometric sequences or geometric progressions.
A geometric sequence is a sequence of numbers in which each term after the first is found by multiplying the previous term by a fixed non-zero number called the common ratio (r). This means that each term in the sequence is obtained by multiplying the previous term by the same constant ratio.
Mathematically, a geometric sequence can be described by the formula:
a, ar, ar^2, ar^3, …
where ‘a’ is the first term and ‘r’ is the common ratio.
For example, let’s consider the geometric sequence:
2, 6, 18, 54, …
In this sequence, the common ratio r can be found by dividing any term by its preceding term.
r = 6/2 = 18/6 = 54/18 = 3
Thus, the common ratio in this sequence is 3. This means that each term in the sequence is obtained by multiplying the previous term by 3.
Understanding the common ratio is essential as it helps in determining the specific term in a geometric sequence, calculating the sum of a geometric series, or finding the limit of the sequence as it approaches infinity.
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