Final answer:
To determine the value of m - n in the given arithmetic sequence, we calculate the common difference which is 10. We then find that n equals 22 and m equals 32, making the value of m - n equal to 10.
Step-by-step explanation:
The question requires us to find the missing terms in an arithmetic sequence and then calculate the difference between them. An arithmetic sequence has a common difference between each term. Given the terms are 12, n, m, 42, we can find the common difference by deducting 12 from 42 and then dividing by 3 (since there are three steps/gaps between 12 and 42).
So, the common difference (d) is (42 - 12) / 3 = 30 / 3 = 10. Therefore, n = 12 + 10 = 22 and m = 22 + 10 = 32. The value of m - n is 32 - 22 = 10.