Class 9 Maths Ganita Manjari Chapter 8 NCERT Solutions: Predicting What Comes Next: Exploring Sequences and Progressions

In mathematics, patterns are everywhere. From number series to real-life situations, recognizing patterns helps us predict what comes next. In Class 9 Maths Ganita Manjari Chapter 8 NCERT Solutions – “Predicting What Comes Next”, students explore the concept of sequences and progressions.

This chapter builds a strong foundation for Arithmetic Progressions (AP) and advanced mathematical concepts used in higher classes.

What is a Sequence?

A sequence is an ordered list of numbers that follow a specific rule.

Examples:

• 2, 4, 6, 8, 10 → Even numbers
• 1, 3, 5, 7 → Odd numbers
• 5, 10, 15, 20 → Multiples of 5

Each number in a sequence is called a term.

NCERT Class 9 Maths Ganita Manjari Chapter 8 Solutions: Download Now
Exercise Set 8.1 (Page 1 - 4)
Exercise Set 8.2 (Page 5 - 7)
Exercise Set 8.3 (Page 8 - 12)
End Of Chapter Exercises (Page 13 - 20)

Identifying Patterns

To understand sequences, we must identify the pattern or rule:

• Addition pattern → +2, +3, etc.
• Multiplication pattern → ×2, ×3, etc.
• Mixed pattern

Example:
3, 6, 9, 12 → Add 3 each time

Arithmetic Progression (AP)

An Arithmetic Progression is a sequence where the difference between consecutive terms is constant.

Formula of AP

an=a+(n−1)da_n = a + (n-1)dan?=a+(n−1)d

Where:

• a = First term
• d = Common difference
• n = Number of terms

Common Difference

d=an−an−1d = a_n - a_{n-1}d=an?−an−1?

Types of Sequences

1. Increasing Sequence

Numbers increase continuously
Example: 2, 4, 6, 8

2. Decreasing Sequence

Numbers decrease
Example: 10, 8, 6, 4

3. Constant Sequence

All terms are same
Example: 5, 5, 5, 5

Solved Examples

Example 1: Find the next term

Sequence: 2, 5, 8, 11
Pattern = +3
Next term = 14

Example 2: Find nth term

Sequence: 3, 6, 9, 12

• a = 3
• d = 3

nth term = 3 + (n−1)×3

Example 3: Find 10th term

Sequence: 5, 10, 15, 20

• a = 5
• d = 5

10th term = 5 + 9×5 = 50

NCERT Exercise Solutions (Sample)

Q1. Identify pattern

Sequence: 1, 4, 7, 10
Answer: AP with d = 3

Q2. Find next term

Sequence: 2, 6, 18
Pattern = ×3
Next term = 54

Q3. Find common difference

Sequence: 7, 10, 13
 d = 3

Real-Life Applications

Sequences and progressions are used in:

• Financial calculations
• Interest calculations
• Construction planning
• Scheduling tasks
• Data analysis

Important Tips

 Always identify the pattern first
Check common difference
Use formulas correctly
Practice different types of sequences

NCERT Class 9 Maths Ganita Manjari Chapter 8 Solutions: Download Now
Exercise Set 8.1 (Page 1 - 4)
Exercise Set 8.2 (Page 5 - 7)
Exercise Set 8.3 (Page 8 - 12)
End Of Chapter Exercises (Page 13 - 20)

Exam Preparation Strategy

• Practice NCERT questions
• Learn formulas thoroughly
• Solve previous year questions
• Focus on conceptual clarity