Figure Series – Study Notes
(Reasoning Ability – NABARD Development Assistant)
1. Simple Explanation
A figure series is a sequence of numbers (or symbols/letters) that follows a hidden pattern.
The task is to identify the rule that generates the series and then predict the next figure(s).
Common patterns:
- Arithmetic or geometric progressions
- Alternating add/subtract or multiply/divide
- Incrementing/decrementing by a fixed number or by a pattern of numbers
- Use of digits’ sum, difference, or product
- Combination of two interleaved sub‑series
The key is to look for regularities in the changes between consecutive figures.
2. Key Points to Remember
| # | What to Look For | How to Test It |
|---|---|---|
| 1 | Arithmetic / Geometric | Check if differences (or ratios) are constant. |
| 2 | Alternating pattern | Split the series into two sub‑series (odd & even positions). |
| 3 | Digit manipulation | Sum of digits, product of digits, reversal, or difference of digits. |
| 4 | Position‑based rule | Multiply or add a value that depends on the position (1, 2, 3, …). |
| 5 | Combination of two rules | One rule for odd terms, another for even terms. |
| 6 | Cyclic pattern | After a certain number of terms the pattern repeats. |
| 7 | Special numbers | Fibonacci, prime numbers, squares, cubes, factorials, etc. |
Tip:
- Write down the series in a table and compute successive differences/ratios.
- Test a few hypotheses quickly; if one fits all terms, that’s likely the rule.
3. Worked Example
Series:
3, 6, 10, 15, 21, 28, 36, ?
Step 1 – Look at differences
| Term | Value | Difference from previous |
|---|---|---|
| 1 | 3 | – |
| 2 | 6 | +3 |
| 3 | 10 | +4 |
| 4 | 15 | +5 |
| 5 | 21 | +6 |
| 6 | 28 | +7 |
| 7 | 36 | +8 |
| 8 | ? | ? |
The differences increase by 1 each time: 3, 4, 5, 6, 7, 8.
Step 2 – Predict next difference
Next difference should be +9.
Step 3 – Find next term
36 + 9 = 45.
Answer: 45
4. Quick Revision Summary
- Identify the rule – arithmetic/geom, alternating, digit‑based, position‑based, or a mix.
- Check differences/ratios to spot constant or progressive changes.
- Split into sub‑series if odd/even terms behave differently.
- Test hypotheses with a few terms; discard any that don’t fit all.
- Compute the next figure using the established rule.
Remember:
- Write down the series; visualizing often reveals hidden patterns.
- Treat each series independently; never assume a “one‑size‑fits‑all” rule.
Good luck!