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Given that 3, p, q, 24 are consecutive terms of an arithmetic progression, we can find the common difference (d) by subtracting the second term from the first term and the third term from the second term:
p - 3 = d
q - p = d
24 - q = d
Since the terms are consecutive, the common difference should be the same:
p - 3 = q - p
q - p = 24 - q
Solving these equations simultaneously gives us:
p = 8
q = 16
Therefore, the value of p is 8 and the value of q is 16.