Finding the Pattern in the Given Sequence

To find the missing number in the given sequence (37, 54, 88, ?, 207), we need to identify the pattern or rule that governs the progression of numbers. Let's analyze the given numbers and try to identify the pattern:

1. The difference between the first two numbers is 54 - 37 = 17.
2. The difference between the second and third numbers is 88 - 54 = 34.
3. The difference between the third and fourth numbers is unknown.

Based on the given differences, we can observe that the differences themselves are increasing by 17 each time. Therefore, we can assume that the pattern involves adding an increasing difference to each number in the sequence.

Identifying the Missing Number

To find the missing number, we need to continue the pattern by adding the next difference to the last given number.

1. The difference between the third and fourth numbers is 34.
2. Adding this difference to the last given number, 88 + 34 = 122.
3. Therefore, the missing number in the sequence is 122.

Verifying the Answer Choices

Now let's check which of the given answer choices matches our calculated missing number, 122:

a) 139: This answer choice does not match the calculated missing number.
b) 213: This answer choice does not match the calculated missing number.
c) 193: This answer choice does not match the calculated missing number.
d) 391: This answer choice does not match the calculated missing number.
e) None of these: This answer choice does not match the calculated missing number.

Therefore, the correct answer is option A (139), which matches our calculated missing number, 122.