Vince wrote the given sequence. (1)/(3),1,(5)/(3),(7)/(3),... Which of the following explains whether the sequence is geometric?
Answer
A
The sequence is geometric because 3 was multiplied to each term to get the next term.
B
The sequence is not geometric because 2 thirds was added to each term to get the next term.
C
The sequence is not geometric because 3 was multiplied to each term to get the next term.
D
The sequence is geometric because 2 thirds was added to each term to get the next term.
Explanation
A geometric sequence has the same ratio between each pair of consecutive terms. Here, each term is found by adding 2/3: 1/3 + 2/3 = 1, and 1 + 2/3 = 5/3. Since the terms are generated by adding a constant amount rather than multiplying by a constant ratio, the sequence is not geometric. Choice B correctly explains this.
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