Counting Sequence

Counting Sequence problems involve patterns where the number of identical shapes (or elements) increases or decreases by a fixed amount each step. You must count the elements in each figure and identify the arithmetic progression to find the next term.

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

Introduction to Counting Sequence

Counting Sequence problems involve patterns where the number of identical shapes (or elements) increases or decreases by a fixed amount each step. You must count the elements in each figure and identify the arithmetic progression to find the next term.

Prerequisites

Counting skills Arithmetic progression concept Visual element counting Basic addition/subtraction
Why This Matters: Counting Sequence problems appear in 1-2 questions in SSC CGL and Banking exams. They test observation and basic arithmetic skills.

How to Solve Counting Sequence Problems

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Step 1: Count the number of elements (shapes) in each figure of the sequence

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Step 2: Write the counts as a number sequence (e.g., 1, 2, 3, 4)

3

Step 3: Find the common difference between consecutive counts

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Step 4: Add the common difference to the last count to get the next count

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Step 5: Visualize or draw the next figure with that many elements

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Step 6: Verify the arrangement pattern if specified (e.g., same shape, same orientation)

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Step 7: Answer with the next figure or its description

Pro Strategy: Count systematically. The pattern is usually arithmetic progression with constant difference. Sometimes the arrangement of elements also follows a pattern (e.g., rows, columns, or random).

Example Problem

Example: Figure 1 has 1 circle, Figure 2 has 2 circles, Figure 3 has 3 circles, Figure 4 has 4 circles. How many circles in Figure 5? Solution: Step 1: Counts: 1, 2, 3, 4 Step 2: Common difference = +1 Step 3: Next count = 4 + 1 = 5 Answer: 5 circles

Pro Tips & Tricks

  • Count elements in each figure carefully—don't miss any
  • The common difference can be positive (increasing) or negative (decreasing)
  • The difference is usually +1, +2, or -1, -2
  • Sometimes the count increases by +1 but the arrangement changes (e.g., from row to triangle formation)
  • For complex arrangements, count by grouping (e.g., by rows or columns)
  • Check if the count pattern is arithmetic, geometric, or follows another sequence

Shortcut Methods to Solve Faster

If counts increase by +1 each time, next count = last count + 1
If counts are 1,3,5,7 → next = 9 (odd numbers)
If counts are 1,4,9,16 → next = 25 (square numbers)
Count pattern often matches position number (1st=1, 2nd=2, 3rd=3...)

Common Mistakes to Avoid

Miscounting elements in complex figures
Assuming the arrangement doesn't matter when it might
Forgetting to check if the difference is constant
Not verifying the pattern with all given terms

Exam Importance

Counting Sequence 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
CAT
0-1 questions
INSURANCE
1-2 questions

Ready to Master Counting Sequence?

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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