observe the first 3 sets of numbers to determine the missing value in the fourth set: (-5,23,12,16) (1, 39,-14,52) (17,47,42,-12) (25,?,11,31)

To determine the missing value in the fourth set, let's examine the pattern in the first three sets of numbers:

Set 1: (-5, 23, 12, 16)
Set 2: (1, 39, -14, 52)
Set 3: (17, 47, 42, -12)

In each set, we can see that the first and fourth numbers are related, as well as the second and third numbers. Let's calculate the differences between these pairs in each set:

Set 1: (16 - (-5)) = 21, (12 - 23) = -11
Set 2: (52 - 1) = 51, (-14 - 39) = -53
Set 3: (-12 - 17) = -29, (42 - 47) = -5

By observing the differences in the first three sets, we can identify a pattern. The first and fourth numbers are decreasing by 5 each time, while the second and third numbers are decreasing by 11 each time.

Now let's apply this pattern to the fourth set, keeping in mind the differences we observed:

Set 4: (25, ?, 11, 31)

To find the missing value, we need to subtract 5 from the first number (25) and add 11 to the third number (11) because of the established pattern:

Missing value = 25 - 5 = 20

Thus, the missing value in the fourth set is 20.