What comes next: 12, 30, 56, 90, 132, ?

Question

What comes next: 12, 30, 56, 90, 132, ?

1. A. 182 (Correct answer)
2. B. 250
3. C. 190
4. D. 293

Correct Answer

Option A — 182

Detailed Solution & Explanation

The correct answer is 182.

Key Points

• Take first differences: 30 − 12 = 18, 56 − 30 = 26, 90 − 56 = 34, 132 − 90 = 42.
• Those differences rise by a constant 8, so the next difference is 50.
• 132 + 50 = 182.
• Equivalently each term is n(n+1) for n = 3, 5, 7, 9, 11, 13 → 13 × 14 = 182.
• When first differences are not constant, take the second differences before guessing.
• Sequences built as n(n+1) — the pronic numbers — appear often; their differences always rise by a constant 2n, which is why the second difference here is a steady 8.

Additional Information

• The terms 12, 30, 56, 90, 132 are pronic numbers, each of the form n(n+1) for n = 3, 5, 7, 9, 11 — the product of two consecutive integers.
• Standard series families to check in order: arithmetic (constant difference), geometric (constant ratio), squares/cubes with an offset, alternating series, and difference-of-difference.
• If first differences are not constant, take second differences before trying anything more elaborate.

प्रश्न (हिन्दी में)

आगे क्या आएगा: 12, 30, 56, 90, 132, ?

1. A. 182
2. B. 250
3. C. 190
4. D. 293