Common Ratio r
In mathematics, the common ratio (r) is a term used to describe the ratio between consecutive terms in a geometric sequence
In mathematics, the common ratio (r) is a term used to describe the ratio between consecutive terms in a geometric sequence.
A geometric sequence is a sequence of numbers where each term, starting from the second term, is obtained by multiplying the previous term by a fixed, non-zero number called the common ratio (r). The formula for finding a term in a geometric sequence is given by:
an = a1 * r^(n-1)
where:
an is the nth term,
a1 is the first term, and
n is the term number.
For example, consider the geometric sequence 2, 6, 18, 54, … The common ratio between the terms is 3, since each term is obtained by multiplying the previous term by 3.
To find any term in this sequence, we can use the formula mentioned earlier. For instance, to find the 5th term, we substitute a1 = 2, r = 3, and n = 5 into the formula:
a5 = 2 * 3^(5-1)
= 2 * 3^4
= 2 * 81
= 162
Therefore, the 5th term of the sequence is 162.
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