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Size Progression

Size Progression problems involve figures that change in size (increase or decrease) following a consistent pattern. The progression can be arithmetic (adding a constant each step) or geometric (multiplying by a constant ratio). You must identify the size pattern and determine the next figure's dimensions.

10Worksheets
200+Practice Questions
BeginnerDifficulty
1-2 hoursHours to Master

What You'll Learn

Introduction & Overview Why This Matters How to Solve Pro Tips & Tricks
Shortcut Methods Common Mistakes Practice Worksheets Exam Importance

Introduction to Size Progression

Size Progression problems involve figures that change in size (increase or decrease) following a consistent pattern. The progression can be arithmetic (adding a constant each step) or geometric (multiplying by a constant ratio). You must identify the size pattern and determine the next figure's dimensions.

Prerequisites

Arithmetic progression concept Geometric progression concept Understanding of scaling factors Basic multiplication and addition
Why This Matters: Size Progression problems appear in 1-2 questions in SSC CGL and Banking PO exams. They test understanding of scaling and proportional reasoning.

How to Solve Size Progression Problems

1

Step 1: Measure or note the size of the figure in each position

2

Step 2: Calculate the difference between consecutive sizes

3

Step 3: If differences are constant → arithmetic progression

4

Step 4: If ratios between consecutive sizes are constant → geometric progression

5

Step 5: For arithmetic: next size = last size + common difference

6

Step 6: For geometric: next size = last size × common ratio

7

Step 7: Select the figure with the calculated size

Pro Strategy: First check if the progression is arithmetic (constant difference) or geometric (constant ratio). For arithmetic, add the same amount each step; for geometric, multiply by the same factor. The shape type usually remains constant.

Example Problem

Example: Square sizes: 20, 28, 36, 44, ___. Find the next size. Solution: Step 1: Sizes: 20, 28, 36, 44 Step 2: Differences: 28-20=8, 36-28=8, 44-36=8 Step 3: Arithmetic progression with difference = 8 Step 4: Next size = 44 + 8 = 52 Answer: Square of size 52 units

Pro Tips & Tricks

  • Arithmetic: sizes form an arithmetic sequence (a, a+d, a+2d, ...)
  • Geometric: sizes form a geometric sequence (a, ar, ar², ...)
  • Size can refer to side length, radius, diameter, or area
  • Watch for size limits (shape may not exceed figure boundaries)
  • The pattern may switch between arithmetic and geometric in complex series
  • Size progression often combines with other transformations

Shortcut Methods to Solve Faster

Arithmetic next size = Last size + (Size₂ - Size₁)
Geometric next size = Last size × (Size₂ ÷ Size₁)
If sizes double each time, ratio = 2
If sizes halve each time, ratio = 0.5

Common Mistakes to Avoid

Confusing arithmetic with geometric progression
Using size values incorrectly (e.g., area vs side length)
Forgetting that shapes may be scaled proportionally in both dimensions
Not verifying the pattern with all given figures

Exam Importance

Size Progression is an important topic for various competitive exams. Here's how frequently it appears:

SSC CGL
1-2 questions
BANKING PO
1-2 questions
RAILWAYS RRB
1-2 questions
INSURANCE
1-2 questions

Ready to Master Size Progression?

Start with Worksheet 1 and work your way up to expert level! Each worksheet includes:

20 practice questions
Detailed solutions
Step-by-step explanations
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