Common ratio
from class:
College Algebra
Definition
The common ratio is the constant factor between consecutive terms of a geometric sequence. It is found by dividing any term by its preceding term.
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5 Must Know Facts For Your Next Test
- The common ratio can be positive, negative, or a fraction.
- In a geometric sequence, each term is obtained by multiplying the previous term by the common ratio.
- If the common ratio is greater than 1, the terms of the sequence will increase; if it's between 0 and 1, they will decrease.
- The formula for the $n$-th term of a geometric sequence is $a_n = a_1 \cdot r^{(n-1)}$, where $a_1$ is the first term and $r$ is the common ratio.
- For an infinite geometric series to converge, the absolute value of the common ratio must be less than 1.
Review Questions
- What is the formula to find the $n$-th term in a geometric sequence?
- How do you determine if a series converges based on its common ratio?
- If you know two consecutive terms in a geometric sequence, how do you find the common ratio?
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