Sequences and Series — Class 11 MCQs with Answers
Class 11 CBSE Mathematics · Chapter 9
90 practice questions · 30 Easy · 30 Medium · 30 Hard · Updated
Practise the most important Class 11 CBSE Mathematics questions from Chapter 9, "Sequences and Series". You get 9 timed quizzes made from 90 NCERT-based MCQs, with answers and explanations. The questions are split into 30 Easy, 30 Medium and 30 Hard. Warm up on the basics, then move on to the exam-level questions that set top scorers in CBSE & Maharashtra HSC Board exams, JEE Main, MHT-CET and JEE Advanced apart.
To score well in "Sequences and Series", focus on fast problem-solving, formula recall and step-by-step working. Each MCQ here is timed and uses exam-style marking (+4 correct, −1 wrong, 0 skipped). This trains you to stay accurate under time pressure, as real papers need. Every question has a short explanation, so a wrong answer becomes a quick lesson. It is the fastest way to fix gaps before a test.
Use this chapter for focused revision. Start with the Easy set to check your basics on Sequences and Series, then move to Medium and Hard to practise applying them. Your accuracy, streaks and XP save automatically. This chapter also adds to your overall Class 11 Mathematics mastery score. 14 sample questions are solved in full below, with the answer and a worked explanation. Sign in free to start practising.
Key concepts: Sequences and Series (Class 11 Mathematics)
A sequence is an ordered list of numbers and a series is their sum. This chapter studies arithmetic progressions with a common difference, geometric progressions with a common ratio, their nth terms and sums, the arithmetic and geometric means with the AM ≥ GM inequality, and the special sums Σn, Σn² and Σn³.
- Sequence and series
- A sequence lists terms in order by a rule; a series adds those terms. Finite sequences end, while infinite ones continue without a last term.
- Arithmetic progression (AP)
- Each term exceeds the previous by a fixed common difference d; the nth term is aₙ = a + (n−1)d, which is linear in n.
- Sum of an AP
- Sₙ = n/2[2a + (n−1)d] = n/2(a + l), where l is the last term; the sum grows quadratically with the number of terms n.
- Arithmetic mean
- The AM of a and b is (a + b)/2; inserting k arithmetic means between two numbers builds an AP with k + 2 terms in total.
Sequences and Series — important questions & MCQs with answers (Class 11 Mathematics)
14 solved questions from this chapter's difficulty levels, each with its answer and explanation. The other 76 are timed and scored when you sign in.
- Q1Easy
nth term of AP a, a+d, a+2d, ... :
A.ndB.a + ndC.a·dⁿ⁻¹D.a + (n−1)d✓ CorrectAnswer: D. a + (n−1)d
Explanation: The nth term of an AP is a + (n−1)d, not a + nd — count n−1 steps from the first term, since a is already term 1 before any step of size d is added.
- Q2Easy
In GP 2, 6, 18, ..., common ratio:
A.4B.3✓ CorrectC.2D.6Answer: B. 3
Explanation: The common ratio is each term divided by the one before: 6/2 = 3 (also 18/6 = 3). Confusing it with the difference 6−2 = 4 gives the wrong AP-style answer.
- Q3Easy
Arithmetic mean of two numbers a and b is:
A.√(ab)B.(a + b)/2✓ CorrectC.2/(1/a + 1/b)D.abAnswer: B. (a + b)/2
Explanation: The arithmetic mean of a and b is their sum halved, (a+b)/2 — the value sitting midway between them. Confusing it with the geometric mean √(ab), which sits midway in ratio rather than difference, is the usual slip.
- Q4Easy
Geometric mean of two positive numbers a and b is:
A.√(ab)✓ CorrectB.(a + b)/2C.a/bD.abAnswer: A. √(ab)
Explanation: The geometric mean of two positive numbers a and b is √(ab), the number whose square equals their product — e.g. GM of 4 and 9 is √36 = 6. Averaging them instead, (a+b)/2 = 6.5, gives the arithmetic mean, a different value.
- Q5Easy
Harmonic mean of two non-zero numbers a and b is:
A.√(ab)B.(a + b)/2C.2ab/(a + b)✓ CorrectD.a + bAnswer: C. 2ab/(a + b)
Explanation: The harmonic mean of a and b is 2ab/(a+b) — e.g. for 4 and 6, HM = 2×24/10 = 4.8. It's the reciprocal of the average of the reciprocals, and it is always the smallest of AM, GM, HM for distinct positive numbers.
- Q6Easy
For positive a, b: AM ≥ GM, with equality iff:
A.a = b✓ CorrectB.a + b = 1C.a · b = 1D.AlwaysAnswer: A. a = b
Explanation: AM ≥ GM turns into equality only when a = b — e.g. a=b=5 gives AM=5=GM. Any spread between the numbers, like 4 and 9 (AM=6.5, GM=6), makes AM strictly greater.
- Q7Medium
Sum of n terms of AP:
A.n·aB.n/2 · [2a + (n−1)d]✓ CorrectC.n·dD.a+ndAnswer: B. n/2 · [2a + (n−1)d]
Explanation: Sₙ = (n/2)[2a + (n−1)d] pairs the first and last term and multiplies by half the count; forgetting the −1 in (n−1)d is the usual slip.
- Q8Medium
Sum of n terms of GP (r≠1):
A.a+rnB.a·rⁿC.a/rD.a(rⁿ−1)/(r−1)✓ CorrectAnswer: D. a(rⁿ−1)/(r−1)
Explanation: For r ≠ 1, Sₙ = a(rⁿ−1)/(r−1) — e.g. GP 1,2,4,8 with a=1, r=2, n=4 gives (16−1)/1=15. Using rⁿ instead of rⁿ−1 in the numerator is the common error.
- Q9Medium
Three arithmetic means are inserted between 3 and 19. The second mean is:
A.15B.9C.11✓ CorrectD.7Answer: C. 11
Explanation: The five terms have common difference (19 − 3)/4 = 4, giving 3, 7, 11, 15, 19.
- Q10Medium
For positive a, b, AM = (a + b)/2 and GM = √(ab). Relation:
A.IndependentB.AM ≤ GMC.AM = GM alwaysD.AM ≥ GM✓ CorrectAnswer: D. AM ≥ GM
Explanation: For any positive a, b, AM ≥ GM always — e.g. a=4, b=16 gives AM=10 ≥ GM=8. They meet only in the special case a=b; otherwise AM stays strictly larger.
- Q11Medium
Σ(k=1 to n) k =
A.n²B.n(n + 1)/2✓ CorrectC.n(n+1)(2n+1)/6D.[n(n+1)/2]²Answer: B. n(n + 1)/2
Explanation: Σk from 1 to n = n(n+1)/2, from Gauss's trick of pairing the sequence with its reverse — e.g. n=4 gives 1+2+3+4=10=4×5/2. Confusing it with Σk² = n(n+1)(2n+1)/6 is the usual mix-up.
- Q12Hard
AM ≥ GM holds for:
A.Negative numbers onlyB.All non-negative reals✓ CorrectC.Integers onlyD.NeverAnswer: B. All non-negative reals
Explanation: AM ≥ GM needs every number ≥ 0 — e.g. 4 and 9 give AM=6.5 ≥ GM=6. With a negative number the square root under GM can turn imaginary, so the inequality breaks down.
- Q13Hard
Sum of infinite GP, |r|<1:
A.a/(1−r)✓ CorrectB.a·rC.a+rD.1/rAnswer: A. a/(1−r)
Explanation: As n→∞, rⁿ→0 only when |r|<1, leaving Sₙ→a/(1−r); e.g. 1+½+¼+...→1/(1−½)=2. For |r|≥1 the series never settles, so no such sum exists.
- Q14Hard
Two numbers have arithmetic mean 10 and geometric mean 8. The larger number is:
A.14B.18C.16✓ CorrectD.12Answer: C. 16
Explanation: The numbers add to 20 and multiply to 64, so they are 16 and 4.
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Start this chapter free →Sequences and Series — FAQs
What are the key concepts in Class 11 Mathematics Sequences and Series?+
A sequence is an ordered list of numbers and a series is their sum. This chapter studies arithmetic progressions with a common difference, geometric progressions with a common ratio, their nth terms and sums, the arithmetic and geometric means with the AM ≥ GM inequality, and the special sums Σn, Σn² and Σn³. Key ideas include Sequence and series, Arithmetic progression (AP), Sum of an AP, Arithmetic mean.
What does Class 11 Mathematics Chapter 9 (Sequences and Series) cover on XamBaaz?+
It has 90 NCERT-based MCQs on "Sequences and Series": 30 Easy, 30 Medium and 30 Hard. Together they make 9 timed quizzes, and you never get the same set twice. Every question has an instant explanation. They help you prepare for CBSE & Maharashtra HSC Board exams, JEE Main, MHT-CET and JEE Advanced.
Are these "Sequences and Series" questions free to practise?+
Yes. Sign in with Google to practise "Sequences and Series" free. Full unlimited access is ₹999/year on a launch offer until 1 December 2026. No chapter is charged separately.
How should I revise "Sequences and Series" for the exam?+
Start with the Easy quiz to check your basics, then try Medium and Hard to practise applying them. There are 9 timed quizzes on this chapter, so you can come back for a fresh set instead of one you have seen. Read each explanation, retry the questions you miss, and track your accuracy until it stays high.
Are these "Sequences and Series" 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 start practising, with instant scoring.
Is there negative marking in the "Sequences and Series" quizzes?+
Yes. The timed quizzes use exam-style marking: +4 for a right answer, −1 for a wrong one and 0 for a skip, the same negative marking as JEE Main and JEE Advanced. MHT-CET and CBSE board papers have no negative marking. Our mocks for those are scored their way.
What are the important questions from Sequences and Series (Class 11 Mathematics)?+
The questions that matter most test Sequence and series, Arithmetic progression (AP), Sum of an AP, Arithmetic mean. This page shows 14 solved important MCQs with answers and explanations; all 90 questions on the chapter are available as timed quizzes once you sign in.
Is there an online quiz for Sequences and Series?+
Yes — Class 11 Mathematics Sequences and Series has timed online quizzes at Easy, Medium and Hard levels, with instant scoring and a worked explanation on every question. The first quiz on the chapter is free.