Direction: What will come in place of the question mark (?) in the following number series? 83, 188, __, 374, 437, 452Options287280487239445

To find the missing number in the series 83, 188, __, 374, 437, 452, we need to determine the pattern or rule that governs the sequence.

Step 1: Calculate the differences between consecutive terms. 188 - 83 = 105 374 - 188 = 186 437 - 374 = 63 452 - 437 = 15

Step 2: Analyze the differences. The differences are 105, 186, 63, and 15. There doesn't seem to be a simple arithmetic progression or geometric progression.

Step 3: Check for a pattern in the differences. 105, 186, 63, 15

Step 4: Consider the possibility of alternating patterns or other sequences. Let's look at the differences between the differences: 186 - 105 = 81 63 - 186 = -123 15 - 63 = -48

Step 5: Check if the differences of differences form a recognizable pattern. 81, -123, -48

Step 6: Since the pattern is not immediately clear, let's try another approach. Consider the possibility of a quadratic or higher-order polynomial sequence.

Step 7: Given the complexity, let's test the options provided: 287, 280, 487, 239, 445

Step 8: Substitute each option into the sequence and check the resulting differences: Option 287: 188 - 83 = 105 287 - 188 = 99 374 - 287 = 87 437 - 374 = 63 452 - 437 = 15

Option 280: 188 - 83 = 105 280 - 188 = 92 374 - 280 = 94 437 - 374 = 63 452 - 437 = 15

Option 487: 188 - 83 = 105 487 - 188 = 299 374 - 487 = -113 437 - 374 = 63 452 - 437 = 15

Option 239: 188 - 83 = 105 239 - 188 = 51 374 - 239 = 135 437 - 374 = 63 452 - 437 = 15

Option 445: 188 - 83 = 105 445 - 188 = 257 374 - 445 = -71 437 - 374 = 63 452 - 437 = 15

Step 9: Evaluate which option fits the pattern best. The option 280 seems to fit the best as the differences are more consistent.

Therefore, the missing number in the series is 280.