Assuming the pattern continues, which one of the following is NOT an arithmetic sequence?

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BlackTom AI · Accepted Answer

Question restatement: The problem asks which of the given sequences, assuming the pattern continues, is NOT an arithmetic sequence.

Option A: 15 1/5, 1, 95 9/5, ... Interpreting the numbers as mixed values, the first term is 15 1/5 (which is 15.2), the second term is 1, and the third term is 95 9/5 (which is 95 + 9/5 = 96.8). The successive differences would be 1 - 15.2 = -14.2 and 96.8 - 1 = 95.8, which are not equal. Since an arithmetic sequence requires a constant difference between consecutive terms, this option does not maintain a fixed step. Therefore, it appears not to be arithmetic. In other words, the gaps are inconsistent, breaking the defining property of arithmetic progressions.

Option B: 60, 180, 300, ... Here the difference between consecutive terms is 120 (180−60 = 120, 300−180 = 120). A constant difference indicates an arithmetic sequence, so this option fits the pattern of an arithmetic progression exactly.

Option C: −2, −9, −16, ... The differences are −7 (−9 − (−2) = −7, −16 − (−9) = −7). Because the step from one term to the next is constant, this is a textbook arithmetic sequence, with common difference −7.

Option D: 2, 4, 8, ... The successive differences are 2 (4−2 = 2) and 4 (8−4 = 4), which are not equal. This means the sequence does not have a constant difference between terms, so it is not arithmetic. The ratio between terms doubles, but arithmetic sequences are defined by constant differences, not constant ratios, so this option fails the arithmetic criterion.

Summary of reasoning across options: A presents inconsistent gaps between terms, breaking the required constant difference of an arithmetic sequence. B exhibits a stable, repeated increment of 120, satisfying the arithmetic condition. C shows a stable increment of −7, also satisfying the arithmetic condition. D shows varying increments (2 then 4), which violates the constant-difference requirement for arithmetic sequences.

MUF0141 Fund. Mathematics Unit 1 - Semester 2, 2025

Assuming the pattern continues, which one of the following is NOT an arithmetic sequence?

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