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Addison is writing a poem. She writes words on the first line, words on the second line, words on the third line, and words on the fourth line. What kind of sequence is this?Choices:(A) arithmetic(B) geometric(C) both(D) neither
Full solution
Q. Addison is writing a poem. She writes words on the first line, words on the second line, words on the third line, and words on the fourth line. What kind of sequence is this?Choices:(A) arithmetic(B) geometric(C) both(D) neither
- Identify Sequence Type: To determine the type of sequence, we need to look at the pattern of the word count in each line. The word counts are , , , and for the first, second, third, and fourth lines, respectively.
- Check for Arithmetic Sequence: We will first check if the sequence is arithmetic by finding the difference between consecutive terms. The difference between the second and the first term is . The difference between the third and the second term is . Since these differences are not the same, the sequence is not arithmetic.
- Check for Geometric Sequence: Next, we will check if the sequence is geometric by finding the ratio between consecutive terms. The ratio of the second to the first term is . The ratio of the third to the second term is . The ratio of the fourth to the third term is . Since these ratios are the same, the sequence is geometric.
