CBSE Class 9 Maths Chapter 8: Predicting What Comes Next: Exploring Sequences and Progressions — Assertion & Reason
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The following Assertion and Reason questions are based on Chapter 8: Predicting What Comes Next: Exploring Sequences and Progressions from the NCERT Class 9 Mathematics textbook. Each question has four options - read both the Assertion (A) and Reason (R) carefully before selecting your answer.
How to attempt Assertion & Reason questions:
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is NOT the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is NOT the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Assertion & Reason Questions
1
Assertion (A): A sequence is an ordered list in which each entry is called a term.
Reason (R): The position of a term is part of the information defining a sequence.
Reason (R): The position of a term is part of the information defining a sequence.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. Changing the order can produce a different sequence even when the same numbers appear.
2
Assertion (A): A sequence may be finite or infinite.
Reason (R): The notation t_n can denote the term in position n.
Reason (R): The notation t_n can denote the term in position n.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both statements are correct, but term notation does not explain whether a sequence ends.
3
Assertion (A): The triangular-number sequence begins 1, 3, 6, 10, 15.
Reason (R): The difference between every pair of consecutive triangular numbers is the same constant.
Reason (R): The difference between every pair of consecutive triangular numbers is the same constant.
Answer: (c)
A is true, but R is false. The successive differences are 2, 3, 4, 5, and so on, so the sequence is not an AP.
4
Assertion (A): The square-number sequence 1, 4, 9, 16, ... is an arithmetic progression.
Reason (R): Its consecutive differences are successive odd numbers rather than one fixed number.
Reason (R): Its consecutive differences are successive odd numbers rather than one fixed number.
Answer: (d)
A is false, but R is true. A changing difference prevents the square numbers from forming an AP.
5
Assertion (A): An explicit rule gives a term directly from its position n.
Reason (R): It does not require calculating all preceding terms first.
Reason (R): It does not require calculating all preceding terms first.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. The position can be substituted directly into the formula.
6
Assertion (A): A recursive rule defines a term using one or more earlier terms.
Reason (R): An explicit rule uses the position number to calculate a term directly.
Reason (R): An explicit rule uses the position number to calculate a term directly.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both definitions are correct, but the explicit-rule definition does not explain the recursive dependence.
7
Assertion (A): Terms of a sequence can be fractions, zero, or negative numbers.
Reason (R): The index n in t_n may take arbitrary negative integer values in an ordinary sequence beginning with its first term.
Reason (R): The index n in t_n may take arbitrary negative integer values in an ordinary sequence beginning with its first term.
Answer: (c)
A is true, but R is false. The usual position index begins with positive integers even when term values themselves are negative.
8
Assertion (A): A recursive formula always gives t_n directly without reference to any earlier term.
Reason (R): A recursive formula uses previous term values together with initial information.
Reason (R): A recursive formula uses previous term values together with initial information.
Answer: (d)
A is false, but R is true. Initial terms and recurrence steps are needed to generate the sequence.
9
Assertion (A): An arithmetic progression is formed by adding a fixed common difference to each term.
Reason (R): A constant additive change makes consecutive differences equal.
Reason (R): A constant additive change makes consecutive differences equal.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. This is the defining property of an AP.
10
Assertion (A): The common difference of an AP can be positive, zero, or negative.
Reason (R): An AP has a linear relationship between term value and position.
Reason (R): An AP has a linear relationship between term value and position.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both are true, but linearity does not explain the range of possible signs of the common difference.
11
Assertion (A): The nth term of an AP with first term a and common difference d is a + (n - 1)d.
Reason (R): The nth term is a + nd because the first term already contains one common difference.
Reason (R): The nth term is a + nd because the first term already contains one common difference.
Answer: (c)
A is true, but R is false. Only n - 1 additions are needed to move from the first term to the nth term.
12
Assertion (A): An arithmetic progression is produced by multiplying each term by a fixed ratio.
Reason (R): A geometric progression, not an AP, is generated by repeated multiplication by a common ratio.
Reason (R): A geometric progression, not an AP, is generated by repeated multiplication by a common ratio.
Answer: (d)
A is false, but R is true. An AP uses a fixed difference, whereas a GP uses a fixed ratio.
13
Assertion (A): The nth term of an AP is t_n = a + (n - 1)d.
Reason (R): The first term corresponds to n = 1 and therefore contributes zero copies of d.
Reason (R): The first term corresponds to n = 1 and therefore contributes zero copies of d.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. After the first term, exactly n - 1 equal increments have occurred.
14
Assertion (A): The nth triangular number is n(n + 1)/2.
Reason (R): The nth square number is the sum of the first n odd numbers.
Reason (R): The nth square number is the sum of the first n odd numbers.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both formulas are true, but the square-number relation does not explain the triangular-number formula.
15
Assertion (A): The sum of the first n natural numbers is n(n + 1)/2.
Reason (R): The sum is n(n - 1)/2 because the first natural number contributes no value.
Reason (R): The sum is n(n - 1)/2 because the first natural number contributes no value.
Answer: (c)
A is true, but R is false. The correct pairing argument gives n(n + 1)/2.
16
Assertion (A): The nth term of a GP is a + (n - 1)r.
Reason (R): For first term a and common ratio r, the nth term is ar^(n - 1).
Reason (R): For first term a and common ratio r, the nth term is ar^(n - 1).
Answer: (d)
A is false, but R is true. Repeated multiplication produces powers of r rather than an additive expression.
17
Assertion (A): A geometric progression is formed by multiplying each term by a fixed common ratio.
Reason (R): Starting from a, repeated multiplication gives a, ar, ar^2, and so on.
Reason (R): Starting from a, repeated multiplication gives a, ar, ar^2, and so on.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. After n - 1 multiplications, the nth term is ar^(n - 1).
18
Assertion (A): Counting retained pieces in constructions such as Sierpinski fractals can produce a geometric progression.
Reason (R): In the Sierpinski square carpet, each retained square produces eight retained squares at the next stage.
Reason (R): In the Sierpinski square carpet, each retained square produces eight retained squares at the next stage.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both statements are true, but the specific carpet example illustrates rather than explains every fractal progression.
19
Assertion (A): A GP has a constant ratio between corresponding consecutive non-zero terms.
Reason (R): The common ratio is found by subtracting a term from the next term.
Reason (R): The common ratio is found by subtracting a term from the next term.
Answer: (c)
A is true, but R is false. Subtraction finds a difference; the GP ratio is obtained by division.
20
Assertion (A): Successive bounce heights that are a fixed fraction of the previous height form an arithmetic progression.
Reason (R): They form a geometric progression because each height is obtained by multiplying by the same fraction.
Reason (R): They form a geometric progression because each height is obtained by multiplying by the same fraction.
Answer: (d)
A is false, but R is true. A constant percentage or fraction creates a fixed ratio, not a fixed difference.
❓ Frequently Asked Questions
What is covered in CBSE Class 9 Maths Chapter 8 Predicting What Comes Next: Exploring Sequences and Progressions?
This chapter covers all key topics from Predicting What Comes Next: Exploring Sequences and Progressions as per CBSE 2026-27 syllabus.
Is this Assertion & Reason useful for CBSE board exams?
Yes, designed for CBSE Class 9 board exam preparation covering the complete syllabus.
Are these CBSE Class 9 Maths Assertion & Reason updated for 2026-27?
Yes, all content at eBookPublisher is updated as per the latest 2026-27 CBSE syllabus.
How many chapters are in CBSE Class 9 Maths?
All chapters of CBSE Class 9 Maths are covered at eBookPublisher with free Assertion & Reason for each chapter.
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