Which of the following statements are true for an geometric pattern? None of the options given are true.The pattern has a constant difference between consecutive terms.The pattern has a constant ratio between consecutive terms.The pattern has a constant second level difference between consecutive terms.
Question
Which of the following statements are true for an geometric pattern? None of the options given are true.The pattern has a constant difference between consecutive terms.The pattern has a constant ratio between consecutive terms.The pattern has a constant second level difference between consecutive terms.
Solution
The statement that is true for a geometric pattern is: "The pattern has a constant ratio between consecutive terms."
In a geometric sequence or pattern, each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio. For example, in the sequence 2, 6, 18, 54, the common ratio is 3, because each term is multiplied by 3 to get the next term.
The other two statements are incorrect in the context of a geometric pattern. "The pattern has a constant difference between consecutive terms" describes an arithmetic sequence, not a geometric one. "The pattern has a constant second level difference between consecutive terms" describes a quadratic sequence.
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