Definition
Common ratio
The fixed multiplier used from one term to the next in a geometric sequence.
Continue from this idea into connected AXIO math.
Defining relationship
Same multiplier, every step.
The common ratio is the fixed number multiplied by each term to make the next term in a geometric sequence.
- term 13× 2
- term 26× 2
- term 312× 2
- term 424
one fixed multiplier
What it means
Look at what you multiply by to move from one term to the next. If that multiplier stays fixed, it is the common ratio. Dividing a term by the previous term finds it only when the previous term is not zero.
Remember it
Same multiplier, every step.
Example
In 64, 32, 16, 8, each term is the term before it multiplied by 1/2. The common ratio is 1/2.
Watch for
The sequence 4, 8, 12 has no common ratio: the multipliers are 2 and then 3/2, so they are not fixed.
Common mix-up
One quotient compares one pair. A common ratio is one multiplier that works for every step.
Exact meaning
The common ratio is the fixed number multiplied by each term to make the next term in a geometric sequence.