Based on the provided reference, the common ratio between successive terms in a geometric sequence is 1/3.
The common ratio of a geometric progression is found by dividing any term by its preceding term. If this ratio is consistent throughout the sequence, it's the common ratio.
Understanding Common Ratio
The common ratio is a key characteristic of a geometric sequence. It represents the constant factor by which each term is multiplied to obtain the next term.
Calculating Common Ratio
Here's how to calculate it, using the reference information:
- Divide consecutive terms: Take any term in the sequence and divide it by the term that comes before it.
- Simplify: Express the resulting fraction in its simplest form.
- Verify consistency: Check if the ratio is the same for different pairs of consecutive terms in the sequence. If it is, then that's your common ratio.
Example
Let's illustrate with a hypothetical geometric sequence: 9, 3, 1, 1/3,...
- Divide: 3 / 9 = 1/3
- Simplify: 1/3 is already in simplest form.
- Verify: 1 / 3 = 1/3 and (1/3) / 1 = 1/3. The common ratio is indeed 1/3.
