Figure series: Reasoning Ability Notes for Uttarakhand Forest Guard

Figure Series – Study Notes

(Uttarakhand Forest Guard – Reasoning Ability – Program 2026)

Figure series are a type of visual pattern recognition question in which a series of shapes (figures) are given.
The task is to find the next figure (or the missing figure) by looking for a hidden rule that governs how the figures change from one term to the next.

1. Simple Explanation

Goal: Identify the rule that transforms each figure into the next one.
Common Transformations
- Shape change (e.g., square → triangle → circle)
- Size change (e.g., increasing or decreasing area or side length)
- Orientation (e.g., rotating 90°, 180°, 270°)
- Color (e.g., black → red → blue)
- Number of sides / components (e.g., number of stars, dots, lines)
- Position (e.g., shifting left/right, moving up/down)
- Combination of the above (e.g., rotate and color change together).

The key is to look for the simplest rule that explains all given terms. If several rules fit, the most “natural” one (fewest steps, simple arithmetic or geometric progression) is usually the right one.

2. Key Points to Remember

#	What to check	How to check	Typical patterns
1	Shape identity	Count vertices, check angles	Triangle → Square → Pentagon → …
2	Size	Compare side lengths or area	1 cm → 2 cm → 3 cm (linear)
3	Orientation	Notice rotation or reflection	0°, 90°, 180°, 270°
4	Color	Observe sequence of colors	Red → Green → Blue → Red
5	Number of figures in a group	Count objects inside the shape	1 dot → 2 dots → 3 dots
6	Position	Track movement on a grid	Left → Right → Up
7	Combination	Check if two or more aspects change together	Rotate 90° + change color

Look for arithmetic or geometric progressions in size, number, angle, or color index.
Use symmetry: many series exploit symmetry (e.g., alternating mirror images).
Avoid over‑complicating: if a simple rule works, you’re likely correct.

3. Worked Example

Question

A series of figures is shown below. Identify the 6th figure.

Figure 1  :  ▲ (red equilateral triangle)
Figure 2  :  ▲ (green equilateral triangle, larger by 1 cm side)
Figure 3  :  ▲ (blue equilateral triangle, larger by 2 cm side)
Figure 4  :  ▲ (red equilateral triangle, larger by 3 cm side)
Figure 5  :  ▲ (green equilateral triangle, larger by 4 cm side)

Options
A. Blue triangle, side +5 cm, red color
B. Red triangle, side +5 cm, green color
C. Green triangle, side +5 cm, blue color
D. Blue triangle, side +5 cm, blue color

Step‑by‑Step Solution

Step	Observation	Reasoning
1	Shape	All figures are equilateral triangles – shape unchanged.
2	Size	Side length increases by +1 cm each step: 1 → 2 → 3 → 4 → 5 cm.
3	Color sequence	Red → Green → Blue → Red → Green → … (cycle of 3).
4	Determine 6th figure	5th is Green, so 6th must be Blue.
5	Size of 6th figure	Next side length = 5 + 1 = 6 cm.
6	Choose correct option	Option D matches: Blue triangle, side +5 cm, color Blue.

Answer – Option D.

4. Quick Revision Summary

Identify the changing attribute(s): shape, size, orientation, color, count, position.
Find the simplest rule: arithmetic or geometric progression, rotation, color cycle, etc.
Check for combinations: sometimes two attributes change together (e.g., rotate 90° and change color).
Confirm with all terms: ensure the rule explains every figure in the series.
Use elimination: if multiple rules fit, choose the one that uses the fewest attributes or simplest numeric pattern.
Practice with varied examples: mix of shape series, color series, size series, and positional series.

Quick Tips for Exam Day

Tip	Why it Helps
Scan the whole series first	Gives a global view of all changes.
Write down observations	Keeps track of shape, size, color, etc.
Look for cycles	Colors, orientations often repeat every 3 or 4 steps.
Check for arithmetic progression	Easy to spot if size or number of components change by constant increments.
Don’t over‑think	If a simple rule works, it’s likely correct.

End of Notes
Happy studying!