A sequence with a common ratio between consecutive terms is called a geometric sequence.
Geometric Sequences Explained
A geometric sequence is defined by a constant ratio between successive terms. This constant ratio is known as the common ratio.
- Definition: A sequence where each term is multiplied by a constant to get the next term.
- Common Ratio (r): The constant value multiplied to each term.
Formula
The general formula for a geometric sequence is:
an = a1 * r(n-1)
Where:
- an is the nth term in the sequence.
- a1 is the first term in the sequence.
- r is the common ratio.
- n is the term number.
Examples of Geometric Sequences
- 2, 4, 8, 16, 32... (common ratio = 2)
- 1, 3, 9, 27, 81... (common ratio = 3)
- 100, 50, 25, 12.5... (common ratio = 0.5)
Identifying Geometric Sequences
To determine if a sequence is geometric, divide any term by its preceding term. If the result is the same for all consecutive pairs of terms, the sequence is geometric.
Common Ratio
As stated in the reference, a geometric sequence is a sequence in which the ratio between any two consecutive terms is a constant. This constant ratio is called the common ratio.
