If (10, 10+d, 10+2d, 10+4d) is an arithmetic progression, which conclusion is correct?

Correct answer: \(d=0\)

The consecutive differences are \((10+d)-10=d\), \((10+2d)-(10+d)=d\), and \((10+4d)-(10+2d)=2d\). In an arithmetic progression, all consecutive differences must be equal. Thus, \(d=2d\), which gives \(d=0\). If \(d=2\) or \(d=4\), the last difference becomes 4 or 8 respectively, so it is not equal to the earlier difference. Exam tip: To test an AP, compare the differences between consecutive terms.