Class 9 CBSE Mathematics — Chapter 8: Predicting What Comes Next?: Exploring Sequences and Progressions MCQs with Answers
90 practice questions · 30 Easy · 30 Medium · 30 Hard
Practise the most important Class 9 CBSE Mathematics questions from Chapter 8, "Predicting What Comes Next?: Exploring Sequences and Progressions" — 9 separately timed quizzes built from 90 NCERT-aligned multiple-choice questions, with answers and explanations. The set is split into 30 Easy, 30 Medium and 30 Hard, so you can warm up on the fundamentals and then push into the exam-level problems that separate top scorers in CBSE Board exams and the JEE & NEET foundation years.
"Predicting What Comes Next?: Exploring Sequences and Progressions" is one of the chapters where problem-solving speed, formula recall and step-by-step reasoning really pays off. Each MCQ on this chapter is timed and uses exam-grade marking (+4 correct, −1 wrong, 0 skipped), training the accuracy-under-pressure that real papers demand. Every question carries a short explanation, so a wrong answer becomes a quick lesson rather than a dead end — the fastest way to close gaps before a test.
Use this chapter as targeted revision: attempt the Easy set first to confirm your basics on Predicting What Comes Next?: Exploring Sequences and Progressions, then move to Medium and Hard to test application and problem-solving. Your accuracy, streaks and XP save automatically, and the chapter feeds into your overall Class 9 Mathematics mastery score. 14 sample questions are solved in full below — answer and worked explanation — and signing in free opens all 90.
Key concepts: Predicting What Comes Next?: Exploring Sequences and Progressions (Class 9 Mathematics)
A sequence is an ordered list of numbers built by a rule. When each term is found by adding a fixed number the sequence is an arithmetic progression; when it is found by multiplying by a fixed number it is a geometric progression. This chapter finds general terms, sums and real-world applications of both.
- Sequence
- An ordered list of numbers following a rule, written a₁, a₂, a₃, … Order matters, so the same numbers in a different order form a different sequence.
- Term and term number
- Each entry is a term; its position n is the term number. aₙ means the nth term, the value in position n.
- Explicit rule
- A formula giving aₙ directly from n, so any term can be found without listing the ones before it.
- Recursive rule
- A rule defining each term from earlier ones, such as aₙ = aₙ₋₁ + aₙ₋₂. It needs starting values before it can generate anything.
Class 9 Mathematics Predicting What Comes Next?: Exploring Sequences and Progressions MCQs with answers
14 solved questions across the difficulty levels this chapter is graded on — answer and explanation shown for each. The remaining 76 are timed and scored when you sign in.
- Q1Easy
What is the common difference of the arithmetic progression 7, 10, 13, 16, …?
A.3✓ CorrectB.2C.4D.7Answer: A. 3
Explanation: The common difference is found by subtracting a term from the next one: d = 10 − 7 = 3. A frequent slip is subtracting in the wrong order or comparing non-consecutive terms.
- Q2Easy
What is the next term of the arithmetic progression 5, 8, 11, 14, …?
A.15B.16C.17✓ CorrectD.18Answer: C. 17
Explanation: Each term adds the common difference d = 8 − 5 = 3, so the next term is 14 + 3 = 17. Don't confuse d with the position number of the term.
- Q3Easy
What is the common ratio of the geometric progression 2, 6, 18, 54, …?
A.2B.3✓ CorrectC.4D.6Answer: B. 3
Explanation: The common ratio is found by dividing a term by the one before it: r = 6 ÷ 2 = 3. Mixing this up with an AP's subtraction gives the wrong value.
- Q4Easy
What is the next term of the geometric progression 3, 6, 12, 24, …?
A.36B.30C.72D.48✓ CorrectAnswer: D. 48
Explanation: The ratio is r = 6 ÷ 3 = 2, so the next term is 24 × 2 = 48. Adding instead of multiplying would wrongly give an AP-style answer.
- Q5Easy
A sequence in which each term is obtained by adding a fixed number to the previous term is called a/an:
A.Harmonic progressionB.Geometric progressionC.Arithmetic progression✓ CorrectD.Random sequenceAnswer: C. Arithmetic progression
Explanation: Repeatedly adding a fixed number defines an arithmetic progression (AP), and that fixed amount is the common difference. Repeatedly multiplying instead gives a geometric progression.
- Q6Easy
A sequence in which each term is obtained by multiplying the previous term by a fixed number is called a/an:
A.Geometric progression✓ CorrectB.Arithmetic progressionC.Linear sequenceD.Constant sequenceAnswer: A. Geometric progression
Explanation: Repeatedly multiplying by a fixed number defines a geometric progression (GP); that fixed multiplier is the common ratio. Adding a fixed number each time is the AP rule instead.
- Q7Medium
What is the 15th term of the AP 3, 7, 11, 15, …?
A.55B.59✓ CorrectC.63D.60Answer: B. 59
Explanation: With a = 3 and d = 4, aₙ = a + (n−1)d gives a₁₅ = 3 + 14×4 = 3 + 56 = 59. Using n = 15 instead of n−1 = 14 in the multiplication overshoots to 63.
- Q8Medium
Which term of the AP 5, 9, 13, … is equal to 41?
A.10th✓ CorrectB.12thC.11thD.9thAnswer: A. 10th
Explanation: Solve 41 = a + (n−1)d with a = 5, d = 4: 36 = 4(n−1), so n − 1 = 9 and n = 10. Forgetting to add 1 back after dividing gives 9 instead of the correct 10.
- Q9Medium
What is the 6th term of the GP 1, 3, 9, 27, …?
A.81B.162C.243✓ CorrectD.729Answer: C. 243
Explanation: With a = 1 and r = 3, aₙ = a·rⁿ⁻¹ gives a₆ = 1 × 3⁵ = 243. Using the exponent 6 instead of 5 would wrongly give 3⁶ = 729.
- Q10Medium
What is the sum of the first 20 natural numbers?
A.200B.210✓ CorrectC.190D.220Answer: B. 210
Explanation: n(n+1)/2 with n = 20 gives 20 × 21 ÷ 2 = 210. Using n = 21 by mistake, or skipping the ÷2, are the usual slips.
- Q11Medium
What is the sum of the first 10 terms of the AP 2, 4, 6, 8, …?
A.110✓ CorrectB.90C.100D.120Answer: A. 110
Explanation: The sum formula Sₙ = n/2[2a + (n−1)d] with a = 2, d = 2, n = 10 gives 5 × [4 + 18] = 5 × 22 = 110. Using n instead of n−1 inside the bracket is the common error.
- Q12Hard
Solving the Tower of Hanoi with 6 disks takes how many more moves than solving it with 5 disks?
A.32✓ CorrectB.31C.16D.63Answer: A. 32
Explanation: Moves for n disks are 2ⁿ − 1: 2⁶ − 1 = 63 for 6 disks and 2⁵ − 1 = 31 for 5 disks, so the difference is 63 − 31 = 32. Subtracting the exponents instead of the move counts gives a meaningless result.
- Q13Hard
What is the sum of all the multiples of 3 from 3 to 99 inclusive?
A.1650B.1620C.1700D.1683✓ CorrectAnswer: D. 1683
Explanation: The terms 3, 6, …, 99 form an AP with a = 3, d = 3, n = 99÷3 = 33. Sum = n/2×(first + last) = 33/2 × 102 = 1683; using n = 99 instead of 33 would badly overshoot.
- Q14Hard
In an AP the 4th term is 11 and the 8th term is 23. What is the 12th term?
A.33B.35✓ CorrectC.37D.39Answer: B. 35
Explanation: a₈ − a₄ = 4d gives d = (23−11)/4 = 3, then a = a₄ − 3d = 11 − 9 = 2, so a₁₂ = 2 + 11×3 = 35. Dividing by 4 correctly, not 5, is the step people skip.
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Start this chapter free →Predicting What Comes Next?: Exploring Sequences and Progressions — FAQs
What are the key concepts in Class 9 Mathematics Predicting What Comes Next?: Exploring Sequences and Progressions?+
A sequence is an ordered list of numbers built by a rule. When each term is found by adding a fixed number the sequence is an arithmetic progression; when it is found by multiplying by a fixed number it is a geometric progression. This chapter finds general terms, sums and real-world applications of both. Key ideas include Sequence, Term and term number, Explicit rule, Recursive rule.
What does Class 9 Mathematics Chapter 8 (Predicting What Comes Next?: Exploring Sequences and Progressions) cover on XamBaaz?+
It covers 90 NCERT-aligned MCQs on "Predicting What Comes Next?: Exploring Sequences and Progressions" — 30 Easy, 30 Medium and 30 Hard — making 9 separately timed quizzes you can sit without ever repeating the same set, each with an instant explanation, suitable for CBSE Board exams and the JEE & NEET foundation years.
Are these "Predicting What Comes Next?: Exploring Sequences and Progressions" questions free to practise?+
Yes — sign in with Google to practise "Predicting What Comes Next?: Exploring Sequences and Progressions" free. Full unlimited access is ₹999/year (limited-time launch price), with no per-chapter charges.
How should I revise "Predicting What Comes Next?: Exploring Sequences and Progressions" for the exam?+
Start with the Easy quiz to confirm your fundamentals, then attempt Medium and Hard for application-level practice. There are 9 separately timed quizzes on this chapter, so you can come back and get a fresh set rather than re-sitting one you have seen. Review each explanation, retry the questions you miss, and track your accuracy on this chapter until it is consistently high.
Are these "Predicting What Comes Next?: Exploring Sequences and Progressions" MCQs available with answers?+
Yes. 14 sample questions are shown here in full, each with the correct option and a step-by-step "Why" explanation. Sign in free with Google to practise all 90 questions with instant scoring.
Is there negative marking in the "Predicting What Comes Next?: Exploring Sequences and Progressions" quizzes?+
Yes — the timed quizzes use exam-grade marking: +4 for a correct answer, −1 for a wrong one and 0 for a skipped question. Note that MHT-CET and the CBSE board papers themselves carry no negative marking — our mocks for those are scored their way, not this way.
Are these important questions for Predicting What Comes Next?: Exploring Sequences and Progressions?+
The set is curated to the NCERT syllabus and weighted toward the question patterns that actually appear in CBSE Board exams and the JEE & NEET foundation years, across Easy, Medium and Hard — so it doubles as an "important questions" revision list for "Predicting What Comes Next?: Exploring Sequences and Progressions".