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Tamil Nadu (TNBSE)Class 7 Mathematics★ 3-6 marks in the TN Class 7 Term 2 exam through pattern and Pascal's-Triangle questions

Information Processing (Term 2) - Pascal's Triangle and Patterns

Samacheer Kalvi (TN State Board) Class 7 Maths — Term 2 Chapter 5, Information Processing. Building and exploring Pascal's Triangle and its patterns, and recognising tables and patterns that lead to linear functions, with worked examples, exercises and quick revision.

⏱ 13 min readEasy difficulty✓ Free · NCERT-aligned

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By the end of this chapter you'll be able to…

1Build Pascal's Triangle
2Identify patterns within Pascal's Triangle
3Find row sums (powers of 2)
4Recognise linear patterns from tables
5Write the rule for a linear pattern

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Why this chapter matters

Spotting and describing number patterns is a key reasoning skill that leads into algebra and functions. Pascal's Triangle and linear patterns are tested in the TN Class 7 Term 2 exam.

Before you start — revise these

A 5-minute refresher here will save you 30 minutes of confusion below.

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Term 1 — Information Processing

Logical reasoning.

Information Processing (Pascal's Triangle and Patterns) — Class 7 Maths (Samacheer Kalvi)

TN State Board (Samacheer Kalvi) Class 7 Mathematics, Term 2 — Chapter 5. Number patterns and the rule behind them.

1. About this chapter

This chapter covers Pascal's Triangle and its patterns, and tables and patterns that lead to linear functions.

2. Pascal's Triangle

Pascal's Triangle is a triangular array of numbers. The top is 1, each row begins and ends with 1, and every other number is the sum of the two numbers above it.

Patterns in it: the outer edges are all 1s; the second diagonal gives the counting numbers (1, 2, 3, 4 …); each row is symmetric; the sum of the numbers in a row doubles each time (1, 2, 4, 8, 16 …).

3. Patterns leading to linear functions

A pattern can often be written as a rule linking the term to its position. If a table shows position n and value, look for a constant difference.
Example: 3, 5, 7, 9 … each rises by 2, so the rule is value = 2n + 1 (a linear pattern).

4. Worked examples

Example 1. Write the next row of Pascal's Triangle after 1 4 6 4 1. Add neighbours and edge 1s → 1 5 10 10 5 1.

Example 2. What is the sum of the numbers in the row 1 3 3 1? 1 + 3 + 3 + 1 = 8 (= 2³).

Example 3. Find the rule for the pattern 4, 7, 10, 13 … Common difference 3, starting near 1 → value = 3n + 1.

5. Exercises (Samacheer Kalvi)

Write the first six rows of Pascal's Triangle.
Find the sum of the numbers in the 5th row (1 4 6 4 1).
Identify the counting numbers in Pascal's Triangle.
Find the rule for the pattern 2, 5, 8, 11 …
Continue the pattern 1, 4, 9, 16 … and state whether it is linear.

6. Common mistakes

Mistake: Forgetting the edge 1s in Pascal's Triangle. Fix: Every row starts and ends with 1.
Mistake: Adding the wrong neighbours. Fix: Each inner number is the sum of the two numbers directly above it.
Mistake: Calling every pattern linear. Fix: A pattern is linear only if the difference is constant (1, 4, 9, 16 is not linear).

7. Quick revision

Term 2 · Ch 5 · information processing.
Pascal's Triangle: edges are 1; each inner number = sum of the two above; rows are symmetric; row sums double (powers of 2).
The second diagonal gives the counting numbers.
A pattern with a constant difference is linear → rule value = (difference)×n + constant.

Key formulas & results

Everything you need to memorise, in one card. Screenshot this for revision.

Pascal's rule

each inner number = sum of the two above

Edges are 1.

Row sum

sum of row n = 2ⁿ

Doubles each row.

Linear pattern

value = (common difference) × n + constant

Constant difference.

Second diagonal

1, 2, 3, 4 … (counting numbers)

Hidden in Pascal's Triangle.

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Common mistakes & fixes

These are the exact errors that cost students marks in board exams. Read them once, save yourself the trouble.

WATCH OUT

✗ Forgetting the edge 1s in Pascal's Triangle

✓ Every row starts and ends with 1.

WATCH OUT

✗ Adding the wrong neighbours

✓ Each inner number is the sum of the two numbers directly above it.

WATCH OUT

✗ Calling every pattern linear

✓ A pattern is linear only if the difference is constant (1, 4, 9, 16 is not linear).

NCERT exercises (with solutions)

Every NCERT exercise from this chapter — what it covers and how many questions to expect.

Pascal's Triangle

Build rows and find patterns and row sums.

Questions

Linear patterns

Find the rule from a table.

Questions

Reasoning

Extend and classify patterns.

Questions

Practice problems

Try each one yourself before tapping "Show solution". Active recall > rereading.

Q1EASY· Pascal

Write the row after 1 4 6 4 1.

▶ Show solution

1 5 10 10 5 1.

Q2EASY· Pascal

Find the sum of the row 1 3 3 1.

▶ Show solution

8 (= 2³).

Q3EASY· Pattern

Find the next term: 2, 5, 8, 11, …

▶ Show solution

14 (difference 3).

Q4MEDIUM· Pattern

Find the rule for the pattern 4, 7, 10, 13 …

▶ Show solution

value = 3n + 1.

Q5MEDIUM· Reasoning

Is the pattern 1, 4, 9, 16 … linear? Why?

▶ Show solution

No; the differences (3, 5, 7) are not constant, so it is not linear (these are square numbers).

Q6EASY· Pascal

Which numbers form the second diagonal of Pascal's Triangle?

▶ Show solution

The counting numbers 1, 2, 3, 4, …

5-minute revision

The whole chapter, distilled. Read this the night before the exam.

•Term 2 Chapter 5 of Samacheer Kalvi Class 7 Maths.
•Pascal's Triangle: edges are 1; each inner number is the sum of the two above.
•Each row is symmetric; row sums double (1, 2, 4, 8 … = powers of 2).
•The second diagonal gives the counting numbers 1, 2, 3, 4 …
•A pattern with a constant difference is linear.
•Rule for a linear pattern: value = (common difference) × n + constant.

Tamil Nadu (TNBSE) marks blueprint

Where the marks come from in this chapter — so you can plan your prep.

Typical chapter weightage: 3-6 marks across pattern questions

Question type	Marks each	Typical count	What it tests
Pascal's Triangle	1-2	1-2	Building rows and row sums
Linear pattern	2	1	Finding the rule
Reasoning	2	1	Classifying patterns

Prep strategy

Practise building Pascal's Triangle row by row
Remember row sums are powers of 2
Check the common difference for linearity
Write the rule as difference×n + constant

Where this shows up in the real world

This chapter isn't just an exam topic — it lives in the world around you.

Probability

Pascal's Triangle gives the numbers in coin-toss outcomes.

Prediction

Linear patterns predict future values.

Computer thinking

Recognising rules underlies algorithms.

Exam strategy

Battle-tested tips from teachers and toppers for this chapter.

Show the edge 1s when building rows
Use 2ⁿ for row sums
Test the common difference for linearity
Express the rule algebraically

Going beyond the textbook

For olympiad aspirants and curious learners — topics that build on this chapter.

Find the sum of the 10th row of Pascal's Triangle without writing it out.
Find the nth-term rule for 5, 9, 13, 17 …

Where else this chapter is tested

CBSE board isn't the only one — other exams test this chapter too.

TN Class 7 Term 2 ExamMedium

Logical Reasoning / OlympiadMedium

School unit testsHigh

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Questions students ask

The real ones — pulled from the Q&A community and tutor sessions.

Except for the 1s on the edges, every number is the sum of the two numbers directly above it in the previous row.

Find the differences between consecutive terms; if that difference is the same throughout, the pattern is linear and can be written as value = difference × n + constant.

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