If (x, x+2, 2x+1) are in an arithmetic progression, what will (d) be?

Correct answer: (2)

The direct answer is option B: \(d=2\). For three terms to be in AP, twice the middle term equals the sum of the first and third: \(2(x+2)=x+(2x+1)\). Expanding gives \(2x+4=3x+1\), so \(x=3\). The terms then are \(3,5,7\), and the common difference is \(5-3=2\), also \(7-5=2\). Option A, 1, is wrong because the terms would not have equal differences. Option B, 2, is correct. Option C, 3, is the value of x, not d; confusing these is a common mistake. Option D, 4, is unsupported and does not match the calculated difference. First find x using the AP condition, then calculate d from consecutive terms.