2, 12, 36, 80, ? — Number & Letter Series Aptitude Question
2, 12, 36, 80, ?: Find the next term: 2, 12, 36, 80, ? Answer and worked solution on CodeKairo.
- Topic: Number & Letter Series
- Section: Logical Reasoning
- Difficulty: Hard
- Time target: 120 seconds
Question
Find the next term:
2, 12, 36, 80, ?
Options
- 120
- 150
- 160
- 180
Show the answer and the worked solution
Correct answer: B. 150
Worked solution
- 1³ + 1² = 2, 2³ + 2² = 12, 3³ + 3² = 36, 4³ + 4² = 80.
- Next = 5³ + 5² = 125 + 25 = 150.
Answer: 150.
The idea
When a term sits between n³ and (n+1)³, try adding a square or a multiple of n to the cube. Testing the smallest terms is fastest.
Shortcut. Factor each term as n² × (n + 1): 1 × 2, 4 × 3, 9 × 4, 16 × 5, so the next is 25 × 6 = 150.
Common trap. 160 — doubling 80 because the terms roughly double near the end; the ratios are falling (6, 3, 2.2), and the true next term, 150, is only about × 1.9.