If the terms (6,6+d,6+2d) become (6,2,-2), what is (d)?

Correct answer: (-4)

The direct answer is option B: d = −4. The displayed terms are 6, 6 + d, and 6 + 2d, and they are said to become 6, 2, −2. Match corresponding terms. The first term already agrees. From the second term, 6 + d = 2. Subtracting 6 from both sides gives d = −4. Verify with the third term: 6 + 2(−4) = 6 − 8 = −2, exactly as required. Option A, 4, would make the terms 6, 10, 14, increasing rather than decreasing. Option B, −4, gives the required sequence and is correct. Option C, 8, gives 6, 14, 22. Option D, −8, gives 6, −2, −10, so the third term is wrong. A negative common difference means that the terms decrease by its positive magnitude.