The Class 9 Maths Chapter 8 Predicting What Comes Next Exploring Sequences and Progressions Worksheet helps CBSE Board students understand how number patterns are formed and how upcoming terms can be predicted using mathematical rules. This worksheet includes practice questions based on sequences, arithmetic progressions, geometric progressions, explicit rules, and recursive rules.
These Worksheets are designed to improve logical thinking and problem-solving skills through different types of questions. Students can use these practice exercises to revise important concepts and check their understanding of the chapter.
Students looking for Class 9 Worksheets can use this chapter worksheet for regular practice, exam preparation, and concept revision. This worksheet follows the latest NCERT Class 9 Maths learning approach and focuses on applying concepts instead of only memorising formulas.
The Class 9 Maths Worksheets collection helps students practise chapter-wise questions with clear solutions, making Maths learning more structured and effective.
Chapter 8 Predicting What Comes Next Exploring Sequences and Progressions Worksheet PDF Download
Get the free Class 9 Maths Chapter 8 Worksheet PDF with important practice questions and step-by-step solutions. Download the worksheet and practise sequences, arithmetic progressions, geometric progressions, explicit rules, and recursive rules anytime for better revision.
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Questions Included in Predicting What Comes Next Exploring Sequences and Progressions Worksheet
A. Remembering Questions
Q1. Define a sequence in Mathematics.
Q2. Write the meaning of the term of a sequence.
Q3. What is an explicit rule in a sequence?
Q4. What is a recursive rule in a sequence?
Q5. Identify the common difference in the given arithmetic progression:
5, 10, 15, 20, ...
Q6. Find the common ratio of the given geometric progression:
3, 6, 12, 24, ...
B. Understanding Questions
Q1. Find the next three terms of the sequence:
7, 14, 21, 28, ...
Q2. A sequence is given by:
tₙ = 4n + 2
Find:
a) 5th term
b) 10th term
Q3. A sequence follows the recursive rule:
First term = 6
Each next term = previous term + 4
Write the first five terms of the sequence.
Q4. Find the missing numbers in the pattern:
12, 18, 24, __, __
Q5. Check whether 55 is a term of the sequence:
5, 10, 15, 20, ...
C. Application Questions
Q1. An arithmetic progression is given:
8, 13, 18, 23, ...
Find the 20th term.
Q2. Find the 15th term of an AP where:
First term (a) = 10
Common difference (d) = 3
Q3. A geometric sequence is:
2, 6, 18, 54, ...
Find the next two terms.
Q4. A plant grows according to this pattern:
Day 1 = 5 cm
Day 2 = 10 cm
Day 3 = 15 cm
If the same pattern continues, find the height of the plant on Day 12.
Q5. A ball is dropped from a height of 64 m. After every bounce, it reaches half of its previous height. Find the height after the 4th bounce.
Worksheet Solutions / Answer Key
Answer 1:
A sequence is an ordered list of numbers arranged according to a specific rule or pattern.
Answer 2:
Each number present in a sequence is called a term of the sequence.
Answer 3:
An explicit rule gives the value of any term directly by using its position number.
Answer 4:
A recursive rule gives the next term by using the previous term of the sequence.
Answer 5: Sequence: 5, 10, 15, 20, ...
Common difference:
10 - 5 = 5
Answer: 5
Answer 6: Sequence: 3, 6, 12, 24, ...
Common ratio:
6 ÷ 3 = 2
Answer: 2
Understanding Question Solutions
Q1. Given sequence:
7, 14, 21, 28, ...
Difference = 7
Next three terms:
35, 42, 49
Q2. Formula:
tₙ = 4n + 2
For 5th term:
t₅ = 4 × 5 + 2
= 20 + 2
= 22
For 10th term:
t₁₀ = 4 × 10 + 2
= 40 + 2
= 42
Q3. First term = 6
Adding 4 each time:
6, 10, 14, 18, 22
Q4. Pattern:
12, 18, 24, __, __
Difference = 6
Missing numbers:
30, 36
Q5. Sequence:
5, 10, 15, 20, ...
55 ÷ 5 = 11
Yes, 55 is the 11th term of the sequence.
Application Question Solutions
Q1. AP:
8, 13, 18, 23, ...
a = 8
d = 5
Formula:
tₙ = a + (n - 1)d
t₂₀ = 8 + (20 - 1) × 5
= 8 + 19 × 5
= 8 + 95
= 103
Answer: 103
Q2. Given:
a = 10
d = 3
t₁₅ = 10 + (15 - 1) × 3
= 10 + 14 × 3
= 10 + 42
= 52
Answer: 52
Q3. Sequence:
2, 6, 18, 54, ...
Common ratio = 3
Next terms:
54 × 3 = 162
162 × 3 = 486
Answer:
162, 486
Q4. Growth pattern:
5, 10, 15, ...
a = 5
d = 5
Day 12:
t₁₂ = 5 + (12 - 1) × 5
= 5 + 55
= 60 cm
Answer: 60 cm
Q5. Initial height = 64 m
After 1st bounce:
64 ÷ 2 = 32 m
After 2nd bounce:
32 ÷ 2 = 16 m
After 3rd bounce:
16 ÷ 2 = 8 m
After 4th bounce:
8 ÷ 2 = 4 m
Answer: 4 m
Skills Developed Through this Worksheet
Practising the Class 9 Maths Chapter 8 Predicting What Comes Next Exploring Sequences and Progressions Worksheet helps students develop:
- Pattern recognition skills
- Logical reasoning ability
- Understanding of mathematical sequences
- Ability to create explicit and recursive rules
- Arithmetic Progression problem-solving skills
- Geometric Progression understanding
- Formula application skills
- Real-life mathematical thinking
Chapter Revision Checklist
Before completing Chapter 8 Predicting What Comes Next Exploring Sequences and Progressions, students should be able to:
- Identify different number patterns
- Understand sequences and their terms
- Find missing numbers in a sequence
- Write explicit rules for sequences
- Use recursive rules correctly
- Find common difference in an AP
- Find common ratio in a GP
- Calculate the nth term of a sequence
- Solve real-life progression-based questions
