What comes next: 0, 6, 24, 60, 120, ?

Question

What comes next: 0, 6, 24, 60, 120, ?

1. A. 196
2. B. 156
3. C. 210 (Correct answer)
4. D. 200

Correct Answer

Option C — 210

Detailed Solution & Explanation

The correct answer is 210.

Key Points

• Each term follows n³ − n for n = 1, 2, 3, …:
  • 1 − 1 = 0, 8 − 2 = 6, 27 − 3 = 24, 64 − 4 = 60, 125 − 5 = 120
• The next term uses n = 6: 216 − 6 = 210.
• Checking by differences agrees: 6, 18, 36, 60 rise by 12, 18, 24, so the next difference is 30 → 120 + 30 = 210... and the second differences confirm 90, giving 210.

Additional Information

• The same terms can be written as (n − 1) × n × (n + 1), the product of three consecutive integers — 0, 1×2×3, 2×3×4, 3×4×5, 4×5×6, 5×6×7 = 210.
• Cubes worth memorising: 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000.
• When a series grows quickly and the differences are not constant, test the cubes and squares with a small offset before attempting anything more elaborate — most SSC series are one of these plus or minus a constant.

प्रश्न (हिन्दी में)

इसके बाद क्या आएगा: 0, 6, 24, 60, 120, ?

1. A. 196
2. B. 156
3. C. 210
4. D. 200