Series – Reasoning Ability (BARC Recruitment)
What is a “Series”?
A series is a list of numbers that follow a particular rule.
In reasoning exams the task is usually to identify the rule and then predict the next term(s).
1. Simple Explanation
| Type | Definition | Example | How to Find Next Term |
|---|---|---|---|
| Arithmetic | Constant difference (d) between consecutive terms. | 3, 7, 11, 15 … | next = last + d |
| Geometric | Constant ratio (r) between consecutive terms. | 2, 6, 18, 54 … | next = last × r |
| Fibonacci‑like | Each term is the sum (or other operation) of the previous two. | 1, 1, 2, 3, 5, 8 … | next = term‑1 + term‑2 |
| Square / Cubic | Terms are perfect squares or cubes. | 1, 4, 9, 16 … | next = (n+1)² |
| Alternating | Two (or more) sub‑series inter‑leaved. | 2, 5, 4, 9, 6, 13 … | Identify each sub‑series separately. |
| Digit‑based | Rule depends on digits (sum, product, reversal, etc.). | 12, 21, 13, 31 … | Apply rule to digits. |
Tip – Always check for differences, ratios, and digit patterns first.
If those don’t reveal anything, look for alternating sub‑series or special number sets (square, prime, factorial).
2. Key Points to Remember
| # | Key Point | Why It Matters |
|---|---|---|
| 1 | Check first differences (term₂ – term₁, term₃ – term₂, …). Constant → Arithmetic. | |
| 2 | Check first ratios (term₂ / term₁, …). Constant → Geometric. | |
| 3 | Look for patterns in digits (sum, product, reversal). Useful for hidden rules. | |
| 4 | Identify alternating patterns (two numbers alternating, or 3‑way, etc.). | |
| 5 | Consider special number sequences (square, cube, prime, Fibonacci, factorial). | |
| 6 | Use “position” logic (n², n(n+1)/2, 2ⁿ, etc.). | |
| 7 | When in doubt, test multiple hypotheses within the exam time limit. | |
| 8 | Cross‑check: once a rule is guessed, verify all terms fit it. | |
| 9 | Beware of “trick” series – sometimes a simple arithmetic rule is hidden under a more complex pattern. | |
| 10 | Practice with past BARC questions – patterns repeat frequently. |
3. Worked Example
Series:
5, 12, 23, 38, 57, …
Step‑by‑Step Solution
| Step | Action | Result |
|---|---|---|
| 1 | Compute first differences: | 12‑5 = 7 23‑12 = 11 38‑23 = 15 57‑38 = 19 |
| 2 | Observe differences: 7, 11, 15, 19 → each increases by 4 | Common difference of differences = 4 |
| 3 | Predict next difference: 19 + 4 = 23 | |
| 4 | Add to last term: 57 + 23 = 80 | Next term = 80 |
Answer: 80
Explanation: The series is quadratic (difference of differences constant).
General formula: aₙ = n² + 4n + 1 (you can derive it by solving for n=1,2,3…).
4. Quick Revision Summary
| Aspect | Quick Check | Example |
|---|---|---|
| Arithmetic | Constant difference? | 4, 9, 14, 19 → d = 5 |
| Geometric | Constant ratio? | 3, 9, 27, 81 → r = 3 |
| Fibonacci‑like | Each = sum of two before? | 2, 3, 5, 8, 13 |
| Squares | Term = n²? | 1, 4, 9, 16, 25 |
| Alternating | Two sub‑series? | 2, 5, 4, 9, 6, 13 |
| Digit rule | Sum/product of digits? | 13, 22 (1+3=4 → 4+18=22) |
| Position rule | n(n+1)/2 or 2ⁿ? | 1, 3, 6, 10 (triangular) |
- Practice: Solve 5‑term series → find next term.
- Time Management: Spend 30 sec on the first two checks (differences & ratios).
- Final Check: Ensure the guessed rule fits all given terms before finalising the answer.
Final Thought
Series questions test pattern recognition and quick arithmetic.
With systematic checking of differences, ratios, digit operations,