Series Completion
Series Completion – 60-Second Refresher
1. Must-Know Patterns
- AP: a, a+d, a+2d … → nth term = a + (n-1)d
- GP: a, ar, ar² … → nth term = arⁿ⁻¹
- HP: reciprocals of AP; 1/2, 1/4, 1/6 …
- Fibonacci: Fₙ = Fₙ₋₁ + Fₙ₋₂ (start 1, 1, 2, 3 …)
- Squares: 1, 4, 9, 16 … (Δ = odd nos. 3,5,7…)
- Cubes: 1, 8, 27, 64 … (Δ² = linear 6,12,18…)
- Prime jump: 2, 3, 5, 7, 11 … (no formula, just recall list)
2. Railway Favourite Tricks
| Type | Quick Check | Mnemonic |
|---|---|---|
| Two-tier series | Operate on alternate terms | “A-B-A-B, treat twins separate” |
| Mixed operator | +, ×, –, ÷ repeating | “PM 9 to 5” (Plus-Mult-Minus-Div) |
| Pair product | (n)(n+1) or (n²–1) | “Naughty-next” |
| Digital root | Sum digits till 1-digit | “DR=9≡0” (same as mod-9) |
3. 3-Step Exam Drill
- Find 1st Δ → constant (AP), linear (square), quadratic (cube)
- Check 2nd Δ → confirms square/cube
- Spot twin alternate → split odd-even positions
4. Last-Minute Tables
| Series | Next Term | Δ | Δ² |
|---|---|---|---|
| 5, 8, 11, 14 | 17 | +3 | 0 |
| 2, 6, 12, 20 | 30 | +4,+6,+8 | +2 |
| 1, 8, 21, 40 | 65 | +7,+13,+19 | +6 |
BETA
