Assertion and Reason Questions For Class 9 Maths Chapter 8: Predicting What Comes Next: Exploring Sequences and Progressions

Assertion-Reason Questions for Class 9 Maths Chapter 8: Predicting What Comes Next: Exploring Sequences and Progressions. These questions help students understand the chapter clearly and also to improve their ability to solve sequence and progression based questions. The content includes the key concepts of the chapter like sequences, arithmetic progression, term patterns and the type of questions that are usually asked in exams. The solutions are prepared thoroughly as per CBSE syllabus and NCERT Textbook to help students in revising well and improving the conceptual understanding. There is also a free downloadable PDF for easy practice and revision.

Assertion and Reason Questions on Class 9 Maths Chapter 8: Predicting What Comes Next: Exploring Sequences and Progressions

Directions: In each question below, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option:

(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.

Q1:

Assertion (A): The sequence 2, 4, 8, 16, … is an AP.

Reason (R): The ratio of consecutive terms is constant.

Answer: D

Explanation: The sequence is not an AP because the difference is not constant. However, it is a GP since the ratio is constant.

Q2: 

Assertion (A): The sequence 6, 12, 24, 48, 96 is a finite sequence.

Reason (R): A finite sequence has a fixed, countable number of terms and does not continue indefinitely.

Answer: (a)

Explanation: Both are true. Unlike infinite sequences, this sequence ends at 96. R correctly defines a finite sequence and explains why A is correct.

Q3:

Assertion (A): The fifth triangular number is 15.

Reason (R): Each triangular number is the sum of natural numbers up to its position. The fifth triangular number = 1 + 2 + 3 + 4 + 5 = 15.

Answer: (a)

Explanation: R gives the defining property of triangular numbers and applies it correctly to confirm A.

Q4:

Assertion (A): The explicit rule for the nth term of the sequence of odd numbers is un = 2n − 1.

Reason (R): Substituting n = 1, 2, 3, 4, … into 2n − 1 gives 1, 3, 5, 7, … which are the odd numbers.

Answer: (a)

Explanation: Both are true and R is the direct verification of A.

Q5:

Assertion (A): The number 471 is a term of the sequence generated by sn = 5n − 2.

Reason (R): To check, we solve 5n − 2 = 471, giving 5n = 473, n = 94.6. Since 94.6 is not a natural number, 471 is NOT a term of the sequence.

Answer: (d)

Explanation: A is false. 471 is not a term of the sequence, making the assertion incorrect as stated. R is true. Hence (d)

Q6:

Assertion (A): The sequence 5, 15/4, 45/16, 135/64, … is a geometric progression with common ratio 3/4.

Reason (R): The ratios of consecutive terms are all equal to 3/4: (15/4) ÷ 5 = 3/4, (45/16) ÷ (15/4) = 3/4, and (135/64) ÷ (45/16) = 3/4.

Answer: (a)

Explanation: Both are true. R performs the three ratio checks and confirms each equals 3/4.

Q7:

Assertion (A): Points obtained from a GP lie on a straight line.

Reason (R): GP terms grow exponentially.

Answer: C

Explanation: Points from a GP usually form a curve, not a straight line. The reason is correct because GP growth is exponential.

Q8:

Assertion (A): In a GP, the difference between consecutive terms is constant.

Reason (R): In a GP, the ratio between consecutive terms is constant.

Answer: D

Explanation: In a GP, the ratio is constant, not the difference.

Q9:

Assertion (A): The sequence 1, –1, 1, –1, … is not a GP.

Reason (R): Its common ratio is –1.

Answer: C

Explanation: The sequence is actually a GP with common ratio –1.

Q10:

Assertion (A): When the terms of an arithmetic progression are plotted as (n, tₙ) coordinates, the points lie on a straight line. But when the terms of a geometric progression are plotted similarly, the points do NOT lie on a straight line.

Reason (R): An AP has a linear nth term formula (tₙ = a + (n−1)d), while a GP has an exponential nth term formula (tₙ = arⁿ⁻¹), and exponential graphs are curves, not straight lines.

Answer: (a)

Explanation: Both are true . AP points are on a straight line while  GP points are on a curve. R correctly attributes this fundamental algebraic difference.

Q11:

Assertion (A): The sum 25 + 26 + 27 + … + 58 = 1411.

Reason (R): This sum equals S₅₈ − S₂₄ = (58 × 59/2) − (24 × 25/2) = 1711 − 300 = 1411.

Answer: (a)

Explanation: Both are true.

Q12:

Assertion (A): The sum of the first 10 natural numbers is 100.

Reason (R): The sum of the first n natural numbers is n(n+1)/2

Answer: C

Explanation: Using the formula, the sum is (10×11)/2 =55, not 100.

Q13:

Assertion (A): In the sequence of square numbers 1, 4, 9, 16, 25, 36, …, the differences between consecutive terms are 3, 5, 7, 9, 11, which are all odd numbers.

Reason (R): Each square number is the sum of consecutive odd numbers: 1 = 1, 4 = 1 + 3, 9 = 1 + 3 + 5, 16 = 1 + 3 + 5 + 7, and so on.

Answer: (a)

Explanation: Both are true and R explains A correctly.

Q14:

Assertion (A): The number 308 is a term of the sequence generated by sn = 5n − 2.

Reason (R): Solving 5n − 2 = 308 gives 5n = 310, so n = 62. Since 62 is a natural number, 308 is the 62nd term.

Answer: (a)

Explanation: Both are true. R performs the check whether a number belongs to a sequence correctly and confirms that 308 is the 62nd termof the given AP.

Q15:

Assertion (A): A sequence is an arithmetic progression (AP) if and only if the difference between any two consecutive terms is constant.

Reason (R): This constant difference is called the common difference, denoted by d, and can be positive, negative, or zero.

Answer: (a)

Explanation: Both are true.R is a complete and accurate explanation of the condition in A.

 

Download the free PDF of Assertion and Reason Questions on Chapter 8: Predicting What Comes Next: Exploring Sequences and Progressions for Class 9 here for quick revision and practice.

Download the PDF: Assertion and Reason Questions on Chapter 8: Predicting What Comes Next: Exploring Sequences and Progressions for Class 9