The following series of numbers is given. One number is missing. Study the pattern and find the missing number. 8, 32, 72, 128, ?

Question

The following series of numbers is given. One number is missing. Study the pattern and find the missing number. 8, 32, 72, 128, ?

1. A. 250
2. B. 200 (Correct answer)
3. C. 228
4. D. 300

Correct Answer

Option B — 200

Detailed Solution & Explanation

The correct answer is 200.

Key Points

• Each term is twice a perfect square of an even number:
  • 8 = 2 × 2², 32 = 2 × 4², 72 = 2 × 6², 128 = 2 × 8²
• Continuing the pattern with 10: 2 × 10² = 2 × 100 = 200.
• Differencing agrees: the gaps are 24, 40, 56, rising by a constant 16, so the next gap is 72 and 128 + 72 = 200.

Additional Information

• Two independent routes reaching 200 is a strong check — where a formula and a difference pattern agree, the reading is almost certainly right.
• Equivalently the terms are 8 × 1², 8 × 2², 8 × 3², 8 × 4², so the next is 8 × 5² = 200; spotting the common factor of 8 is often the quickest way in.
• Constant second differences always indicate a quadratic pattern, which is why a square-based rule was worth trying first.
• Squares to have ready: 4, 16, 36, 64, 100, 144 — doubling them gives exactly this series.