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5,-15,45,-60

is this arithmetic geometic or neither

1 answer

To determine whether the sequence \(5, -15, 45, -60\) is arithmetic, geometric, or neither, we need to analyze the relationships between the terms.

  1. Arithmetic Sequence: A sequence is arithmetic if the difference between consecutive terms is constant.

    • First difference: \(-15 - 5 = -20\)
    • Second difference: \(45 - (-15) = 60\)
    • Third difference: \(-60 - 45 = -105\)

    The differences are not constant, so the sequence is not arithmetic.

  2. Geometric Sequence: A sequence is geometric if the ratio between consecutive terms is constant.

    • First ratio: \(-15 / 5 = -3\)
    • Second ratio: \(45 / (-15) = -3\)
    • Third ratio: \(-60 / 45 = -4/3\)

    The ratios are also not constant, so the sequence is not geometric.

Since the sequence is neither arithmetic nor geometric, we conclude that it is neither.