If the terms (4, 4+d, 4+2d) become (4, 1, −2), what is d?

Correct answer: −3

The governing concept is the general form of an arithmetic progression. In three consecutive terms written as a, a+d, a+2d, the constant d is the common difference between successive terms. Comparing the given first two terms, 4+d=1, so subtracting 4 from both sides gives d=−3. This result is confirmed by the third term: 4+2d=4+2(−3)=4−6=−2, exactly as required. Therefore option B is correct. Option A has the wrong sign and would produce the sequence 4,7,10. Option C would make the second term 9, and option D would make the second term −1, so neither matches the supplied terms. The negative value simply means that the arithmetic progression decreases by 3 at each step.