Study Notes – Figure Series
Program: Agniveer
Subject: Reasoning Ability
Topic: Figure Series
1. Simple Explanation
A figure series is a sequence of geometric figures (shapes, patterns, or arrangements) that follow a clear rule or logic.
Your job is to:
- Identify the rule that transforms one figure into the next.
- Apply that rule to the last figure in the series to predict the next one.
The rule can involve any of the following transformations:
| Transformation | What it does | Example |
|---|---|---|
| Rotation | Turn the figure by a fixed angle (90°, 180°, etc.). | A square → rotated 90° → same square. |
| Reflection | Flip the figure over an axis. | A triangle → mirrored left‑to‑right. |
| Scaling | Change the size (enlarge or shrink). | A circle → twice the radius. |
| Translation | Move the figure without rotating. | A rectangle → shifted right by 2 units. |
| Addition/Subtraction of elements | Add or remove shapes or lines. | A square → add a diagonal line. |
| Color change | Switch colors or shading. | A black shape → turns gray. |
| Rotation + Scaling | Combination of two above. | A triangle → rotate 60° and double size. |
The key is to spot one consistent rule that applies from figure 1 → figure 2 → figure 3 → …
2. Key Points to Remember
| # | Point | Why it matters |
|---|---|---|
| 1 | Look for symmetry | Symmetry often hints at reflection or rotation. |
| 2 | Count elements | Number of sides, vertices, or lines can change systematically. |
| 3 | Check orientation | Position of shapes relative to axes or to each other. |
| 4 | Observe color or shading changes | May indicate a separate rule (color alternation). |
| 5 | Consider the sequence length | Short sequences may hide a simple rule; long ones might combine multiple. |
| 6 | Use elimination | If a rule doesn’t fit all transitions, discard it. |
| 7 | Remember “no change” | Sometimes the figure stays the same (identity operation). |
| 8 | Look for “cumulative” changes | Each step might build on the previous one (e.g., add one more line). |
| 9 | Check for 2D vs 3D | Some series involve 3‑D shapes (cubes, pyramids). |
| 10 | Remember exam constraints | Usually 4–5 figures are shown; avoid over‑complicating. |
3. Worked Example
Prompt
Sequence:
1️⃣ Figure A: A blue square.
2️⃣ Figure B: The same square, rotated 90° clockwise.
3️⃣ Figure C: The square rotated 90° again, now turned red.
4️⃣ Figure D: The square rotated 90° again, color back to blue.Question: What will Figure 5 look like?
Step‑by‑Step Solution
| Step | Observation | Rule Deduction |
|---|---|---|
| 1 | A square → rotate 90° → same shape. | Rotation by 90° each step. |
| 2 | Color alternates: blue → red → blue. | Color alternation every two steps (or every step). |
| 3 | Size remains constant. | No scaling. |
| 4 | All transformations are independent. | Combined rule: Rotate 90° clockwise and toggle color between blue and red. |
Apply the rule to Figure D:
- Rotation: Figure D is already rotated 90° from Figure C. Rotate it another 90° → total 270° from original orientation.
- Color: Color toggles each step. Since Figure D is blue, Figure 5 will be red.
Result:
- A blue square rotated 270° (which visually looks the same as the original square).
- Color: red.
Answer: A red square (orientation visually identical to the original, but color changed).
4. Quick Revision Summary
- Identify the basic transformation(s): rotation, reflection, scaling, translation, element addition, color change.
- Check consistency across all given figures.
- Look for patterns in number/size/position of elements.
- Apply the deduced rule to the last figure to predict the next.
- Double‑check that the predicted figure satisfies all rules simultaneously.
Practice Tip
Draw the series on paper.
- Mark the axis, center, and orientation of each figure.
- Use arrows to show rotations or translations.
- Color the figures differently if color is part of the rule.
Doing this visually helps you spot the rule faster during exams.
Good luck with your Agniveer preparation!