If (12, b, 2b-3, 39) are in an arithmetic progression, what is the value of (b)?

Correct answer: (21)

In an arithmetic progression, the difference between every pair of consecutive terms is the same. Here the four terms are 12, b, 2b−3, and 39. Because there are four terms, the change from the first term to the fourth term contains three equal common differences. This lets us determine the common difference before finding b.

The total change is 39−12=27. Therefore, the common difference is \(d=27/3=9\). The second term is one common difference after the first, so \(b=12+9=21\). Checking the next term gives \(2b−3=2(21)−3=39\), which is consistent with the fourth term. Thus option C, 21, is correct. A value such as 20 would not produce equal consecutive differences.