Find the missing term in the series and choose the correct option: 4, 8, 24, 60, ?, 224. Hint: differences are squares of even numbers.

Difficulty: Easy

Correct Answer: None of these

Explanation:

Introduction / Context:This completion problem relies on recognizing a pattern in successive differences, specifically perfect squares of even integers.

Given Data / Assumptions:

  • Series: 4, 8, 24, 60, ?, 224.
  • Expect regular, easily described differences.

Concept / Approach:Compute differences and check for square numbers: 8 − 4, 24 − 8, 60 − 24, …

Step-by-Step Solution:

8 − 4 = 4 = 2^224 − 8 = 16 = 4^260 − 24 = 36 = 6^2Next difference should be 8^2 = 64, so missing term = 60 + 64 = 124.Final difference 224 − 124 = 100 = 10^2, which fits the even-square ladder (2, 4, 6, 8, 10).

Verification / Alternative check:The even-square progression is uniquely neat and yields a self-consistent completion.

Why Other Options Are Wrong:178, 96, 109, 141 do not preserve the even-square sequence; only 124 would, but it is not among the listed options.

Common Pitfalls:Trying multiplicative rules; here, additive square steps are more natural.

Final Answer:The correct missing value is 124, which is not present among the options; hence None of these.

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