Figure Series – Quick & Easy Study Notes
(For the Tripura Police SI Reasoning Ability Test)
1. What is a Figure Series?
A figure series is a line of shapes that follow a rule.
Think of it like a pattern of beads on a necklace.
If you know how the beads are arranged, you can guess the next one.
2. Why It Matters
- Time‑saving: A clear rule lets you answer fast.
- Score‑boosting: Many SI papers have a few figure‑series questions.
3. Common Types of Rules
| Rule | Everyday Analogy | How to Spot It |
|---|---|---|
| 1. Count the number of elements | Counting apples in a basket | Look at how many shapes appear in each row or column. |
| 2. Size change (increase/decrease) | Growing plant leaves | Notice if shapes get bigger or smaller. |
| 3. Color change | Changing traffic lights (red → yellow → green) | Observe any color shift pattern. |
| 4. Rotation | Turning a fan blade | Shapes turn clockwise or counter‑clockwise. |
| 5. Reflection / Mirror | Looking at yourself in a mirror | Shapes look like a flipped copy. |
| 6. Adding/Removing shapes | Building a tower with blocks | Shapes are added or removed one by one. |
| 7. Alternating pattern | Two‑step dance (step, skip, step, skip) | Two or more different elements repeat in a cycle. |
| 8. Symmetry | Mirror‑image word “LEVEL” | Left side mirrors the right side. |
| 9. Combination of the above | A recipe that mixes multiple steps | Several rules work together. |
4. Step‑by‑Step Solving Guide
- Look at the whole series – Not just the first two terms.
- Count shapes in each term – 3 circles, 5 squares, etc.
- Check size – Are they getting larger or smaller?
- Check color – Any color cycle?
- Check orientation – Are they rotated?
- Check symmetry – Do the left and right halves mirror each other?
- Identify the simplest rule – Start with the rule that requires the least effort.
- Apply the rule to find the next term – Write it down.
- Cross‑check – Does the next term fit all the rules you found?
5. Tiny Example
Series:
| 1 | 2 | 3 | 4 |
|---|---|---|---|
| ● | ●● | ●●● | ●●●● |
- Rule: Number of circles increases by 1 each time.
- Next term: 5 circles → ●●●●●
6. Quick Tips
- Pattern in the first 2–3 terms is usually enough.
- If you’re stuck, try “counting” first – How many shapes?
- Look for symmetry first – It’s hard to miss.
- Remember simple math tricks:
- Even/Odd → 2, 4, 6…
- Square numbers → 1, 4, 9…
- Triangular numbers → 1, 3, 6…
7. Practice Problems
Problem 1
- ○
- ○○
- ○○○
- ○○○○
Find the 5th term.
Problem 2
- △
- △△
- △△△
- △△△△
Find the 5th term.
Problem 3
- ▲ ▲
- ▲ ▲ ▲
- ▲ ▲ ▲ ▲
- ▲ ▲ ▲ ▲ ▲
Find the 5th term.
Problem 4
- ● → ▲
- ● ● → ▲ ▲
- ● ● ● → ▲ ▲ ▲
- ● ● ● ● → ▲ ▲ ▲ ▲
Find the 5th term.
Problem 5
- ○ ○
- ○ ○ ○
- ○ ○ ○ ○
- ○ ○ ○ ○ ○
Find the 5th term.
8. Solutions
| # | Answer | Explanation |
|---|---|---|
| 1 | ●●●●● | Number of circles keeps increasing by 1. |
| 2 | △△△△△ | Number of triangles keeps increasing by 1. |
| 3 | ▲ ▲ ▲ ▲ ▲ | Number of triangles keeps increasing by 1. |
| 4 | ● ● ● ● ● → ▲ ▲ ▲ ▲ ▲ | 5 circles → 5 triangles. |
| 5 | ○ ○ ○ ○ ○ ○ | Number of circles keeps increasing by 1. |
9. Final Checklist Before the Exam
- Identify the first rule (count, size, color, etc.).
- Look for any symmetry or mirroring.
- Be careful of two‑step cycles (e.g., red, blue, red, blue).
- Double‑check the answer by seeing if it fits all patterns you spotted.
Remember
Figure series problems are just puzzles waiting for a pattern. Treat them like a story: read the first few “chapters” (terms) and guess what will happen next. With practice, you’ll spot the rule in seconds. Good luck!