Quick answer: For a GP with nonzero terms, the common ratio is next term divided by previous term. A negative ratio alternates the signs. Verify the same ratio across consecutive pairs.
Worked example
Find the ratio and next term of 3, −6, 12, −24.
- −6/3 = −2 and 12/(−6) = −2.
- Also −24/12 = −2, confirming a constant ratio.
- Multiply −24 by −2 to get the next term, 48.
Check the result
Dividing 48 by −24 again gives −2.
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Common mistake to avoid
Division by zero is undefined. A sequence such as 5, 0, 0 can be generated with r = 0, but the later ratio 0/0 cannot be used to calculate r.
Try it yourself
1. Find r for 81, 27, 9. 2. Is 2, 4, 7 a GP?
Answers and reasoning
1. r = 1/3. 2. No: 4/2 = 2 while 7/4 = 1.75.
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