NCERT Class 9 Mathematics Ganita Manjari: Chapter 8 — Predicting What Comes Next: Exploring Sequences and Progressions
This chapter introduces students to the concept of sequences and progressions in Mathematics, focusing on patterns and prediction. It begins by highlighting the prevalence of patterns in everyday life and their importance in making sense of the world and predicting future events. The chapter defines a sequence as an ordered list of numbers, where each number is a term. It revisits familiar number sequences like natural numbers, odd numbers, triangular numbers, and square numbers, emphasizing that these sequences can be finite or infinite. Students are encouraged to identify patterns and predict the next terms in these sequences. The chapter also explores the relationship between triangular numbers and sums of natural numbers, and between square numbers and sums of odd numbers, using visual representations to aid understanding. This foundational knowledge in sequences is crucial for further study in mathematics and problem-solving.
Quick info
| Board | CBSE / NCERT |
|---|---|
| Class | Class 9 |
| Subject | Mathematics |
| Book | Ganita Manjari |
| Chapter | Chapter 8 — Predicting What Comes Next: Exploring Sequences and Progressions |
| Language | English |
| PDF type | NCERT Textbook |
| Session | CBSE 2026 |
| Reading time | 4 minutes |
| Word count | 625 |
Learning outcomes
- Identify and describe patterns in number sequences.
- Define a sequence and its terms.
- Distinguish between finite and infinite sequences.
- Predict the next terms in known number sequences.
- Understand the relationship between triangular numbers and sums of natural numbers.
- Understand the relationship between square numbers and sums of odd numbers.
Vocabulary
| Word | Meaning |
|---|---|
| Sequence | An ordered list of numbers where each number is a term. |
| Term | Each number in a sequence. |
| Finite sequence | A sequence with a limited number of terms. |
| Infinite sequence | A sequence that continues indefinitely. |
| Natural Numbers | The set of positive integers: 1, 2, 3,... |
| Odd Numbers | Integers not divisible by 2: 1, 3, 5,... |
| Triangular Numbers | Numbers represented by triangular arrays of dots, formed by summing consecutive natural numbers. |
| Square Numbers | Numbers obtained by squaring an integer (n²), formed by summing consecutive odd numbers. |
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Practice questions
- What is a sequence? Answer: A sequence is an ordered list of numbers where each number is a term of the sequence.
- Give an example of an infinite sequence. Answer: The sequence of natural numbers (1, 2, 3,...) is an example of an infinite sequence.
- What is the pattern in the sequence of odd numbers? Answer: The pattern is that each term is 2 more than the previous term.
- How are triangular numbers formed? Answer: Triangular numbers are formed by summing consecutive natural numbers (e.g., 1, 1+2, 1+2+3,...).
- What is the fifth term in the sequence of square numbers? Answer: The fifth term is 25 (since 5² = 25).
Frequently asked questions
What is the main idea of Chapter 8 in NCERT Class 9 Mathematics?
Chapter 8 introduces sequences and progressions, focusing on identifying patterns in numbers and predicting what comes next.
What is a sequence in mathematics?
A sequence is an ordered list of numbers where each number is called a term.
Can you give an example of a finite sequence?
Yes, the sequence 6, 12, 24, 48, 96 is a finite sequence with five terms.
What are triangular numbers?
Triangular numbers are numbers that can be arranged in a triangular pattern, formed by summing consecutive natural numbers (e.g., 1, 3, 6, 10).
How are square numbers related to odd numbers?
Each square number is the sum of consecutive odd numbers starting from 1 (e.g., 1=1, 4=1+3, 9=1+3+5).
Why are patterns important in mathematics?
Patterns help us understand the world, make sense of data, and predict future outcomes or values.
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NCERT Class 9 Mathematics — Ganita Manjari — Chapter 8 — Predicting What Comes Next: Exploring Sequences and Progressions. Verified by NCERT Help Editorial Team. Reviewed on 29 Jul 2026. Last updated 10 Aug 2026.