If the second term is (11) and the fourth term is (21) in (6, 6+d, 6+2d, 6+3d), what is (d)?

Correct answer: (5)

The direct answer is option B: \(d=5\). The displayed AP is \(6,6+d,6+2d,6+3d\), so each next term increases by d. The second term is given as 11, hence \(6+d=11\). Subtracting 6 from both sides gives \(d=5\). Check the fourth term: \(6+3d=6+3(5)=21\), exactly as required. Option A, 4, would make the second term 10, not 11. Option B, 5, makes both given conditions true, so it is correct. Option C, 6, would make the second term 12 and the fourth 24. Option D, 7, would make them 13 and 27. The common difference is the fixed amount added between consecutive terms. Memory cue: use the simplest given term first, then verify every other condition.