TRUE. An arithmetic sequence is defined by having a constant difference between consecutive terms. As long as you add the same value each time, the sequence is arithmetic. Original sequence: a, a + d, a + 2d, a + 3d, ... (common difference = d). New sequence: 2a, 2a + d/2, 2a + 2(d/2), 2a + 3(d/2), ... which is 2a, 2a + d/2, 2a + d, 2a + 3d/2, ... Check differences: (2a + d/2) - 2a = d/2, (2a + d) - (2a + d/2) = d/2, (2a + 3d/2) - (2a + d) = d/2. The new common difference is d/2 (constant throughout), so the new sequence IS arithmetic. Changing the first term (doubling it) doesn't affect the pattern of differences—it just shifts where the sequence starts. Changing the common difference (halving it) changes how fast the sequence grows, but it's still arithmetic as long as the difference remains constant. This conceptual question tests deep understanding and might appear in ECZ Paper 1 as a true/false or in Paper 2 as part of a proof question.

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• ivwananji siwale – 29 pts

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