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

Question

BlackTom AI · Accepted Answer

To assess whether each sequence is arithmetic, we check if the difference between consecutive terms stays the same across the sequence.
Option a: –5, −10, –20, … The differences are −5 (from –5 to −10) and −10 (from −10 to −20), which are not equal. This breaks the constant-difference rule, so this sequence is not arithmetic.
Option b: 3, 9, 15, … Here the successive differences are +6 (9−3 and 15−9), which remain constant. This satisfies the arithmetic sequence condition.
Option c: 3, 6, 9, … The successive differences are +3 (6−3 and 9−6), again constant, so this is an arithmetic sequence.
Option d: 6, 36, 66, … The differences are +30 (36−6) and +30 (66−36), which are equal, fulfilling the constant-difference criterion. This is also an arithmetic sequence.
Thus, evaluating all options shows that the only sequence failing the arithmetic condition is the first one, due to its non-constant differences.

MUF0141 Fund. Mathematics Unit 1 - Semester 2, 2025 5.6 Arithmetic Sequences Quiz (Formative)

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

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