Arithmetic Progressions — Class 10 MCQs with Answers
Class 10 CBSE Mathematics · Chapter 5
90 practice questions · 30 Easy · 30 Medium · 30 Hard · Updated
Practise the most important Class 10 CBSE Mathematics questions from Chapter 5, "Arithmetic Progressions". 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 Board exams and the JEE & NEET foundation years apart.
To score well in "Arithmetic Progressions", 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 Arithmetic Progressions, 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 10 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: Arithmetic Progressions (Class 10 Mathematics)
An arithmetic progression is a list in which each term differs from the previous one by a fixed amount. This chapter finds any term directly, sums the first n terms, and applies both to problems about instalments, savings and patterns.
- Arithmetic progression (AP)
- A sequence in which the difference between any term and the one before it is constant throughout.
- Common difference (d)
- The fixed gap between consecutive terms, found as aₙ − aₙ₋₁. A negative d makes the sequence decrease.
- First term (a)
- The starting value of the AP, from which every other term is generated by repeatedly adding d.
- General (nth) term
- aₙ = a + (n − 1)d gives any term directly, without listing all the terms before it.
Arithmetic Progressions — important questions & MCQs with answers (Class 10 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
Common difference of the AP 5, 8, 11, 14, … is:
A.2B.−3C.5D.3✓ CorrectAnswer: D. 3
Explanation: Common difference d = term − previous term: d = 8 − 5 = 3, and the same gap of 3 repeats through 11, 14, confirming a genuine AP.
- Q2Easy
In an AP, the common difference d is:
A.a₂ − a₁✓ CorrectB.a₁ + a₂C.a₁/a₂D.a₁ × a₂Answer: A. a₂ − a₁
Explanation: By definition, the common difference is any term minus the one right before it, d = a₂ − a₁ — not a sum, ratio, or product of terms.
- Q3Easy
Sum of first n terms of AP is:
A.n[2a + (n − 1)d]B.(n/2)[a + (n − 1)d]C.(n/2)[2a + (n − 1)d]✓ CorrectD.a + (n − 1)dAnswer: C. (n/2)[2a + (n − 1)d]
Explanation: The standard sum formula is Sₙ = (n/2)[2a + (n − 1)d] — dropping the (n − 1)d term or the factor of 2 gives the wrong distractor formulas.
- Q4Easy
The sum of the first 10 terms of the AP 1, 3, 5, 7, … is:
A.110B.90C.100✓ CorrectD.121Answer: C. 100
Explanation: The first ten odd numbers add to 100, agreeing with (10/2)(2 × 1 + 9 × 2).
- Q5Easy
The 10th term of the AP 2, 5, 8, … is:
A.30B.32C.29✓ CorrectD.27Answer: C. 29
Explanation: Use aₙ = a + (n − 1)d with a = 2, d = 3: a₁₀ = 2 + 9 × 3 = 29. Forgetting to subtract 1 from n gives a wrong multiple of d.
- Q6Easy
Which is an AP?
A.2, 4, 8, 16...B.2, 4, 6, 8...✓ CorrectC.1, 4, 9, 16...D.1, 1/2, 1/3...Answer: B. 2, 4, 6, 8...
Explanation: An AP must add the same amount each step: 2, 4, 6, 8 has a constant d = 2, while the other sequences double, square, or use reciprocals instead.
- Q7Medium
Which term of the AP 21, 18, 15, … is zero?
A.7thB.8th✓ CorrectC.9thD.10thAnswer: B. 8th
Explanation: Here a = 21, d = −3. Set aₙ = 0: 21 + (n − 1)(−3) = 0 → n − 1 = 7 → n = 8, so the 8th term is the first to reach zero.
- Q8Medium
Sum of three numbers in AP is 24 and product is 440. The numbers are:
A.6, 8, 10B.5, 8, 11✓ CorrectC.4, 8, 12D.2, 8, 14Answer: B. 5, 8, 11
Explanation: Take the numbers as a − d, a, a + d: their sum 3a = 24 gives a = 8, and the product 8(64 − d²) = 440 gives d² = 9, so d = 3 and the numbers are 5, 8, 11.
- Q9Medium
Sum of first n terms of AP 9, 17, 25... is 636. Then n is:
A.12✓ CorrectB.11C.10D.13Answer: A. 12
Explanation: Sₙ = (n/2)[2a + (n − 1)d] with a = 9, d = 8 gives n(4n + 5) = 636, a quadratic that factors as (n − 12)(4n + 53) = 0, so n = 12.
- Q10Medium
The sum of the first 20 natural numbers is:
A.190B.200C.220D.210✓ CorrectAnswer: D. 210
Explanation: Sum of first n natural numbers: Sₙ = n(n+1)/2 = 20 × 21/2 = 210. Forgetting to divide by 2 gives the tempting but wrong 420-style overcount.
- Q11Medium
The 15th term of AP −2, −5, −8... is:
A.−44✓ CorrectB.−47C.−41D.−38Answer: A. −44
Explanation: aₙ = a + (n − 1)d with a = −2, d = −3: a₁₅ = −2 + 14 × (−3) = −2 − 42 = −44.
- Q12Hard
If the 5th term of an AP is 20 and the 9th term is 36, then the first term is:
A.0B.4✓ CorrectC.2D.8Answer: B. 4
Explanation: Write a + 4d = 20 and a + 8d = 36; subtracting gives 4d = 16, so d = 4, and a = 20 − 4×4 = 4.
- Q13Hard
If a, b, c are in AP, then which is true?
A.b − a = c − bB.2b = a + cC.b = (a + c)/2D.All of the above✓ CorrectAnswer: D. All of the above
Explanation: In an AP, the middle term equals the average of its neighbours: b − a = c − b, which rearranges to 2b = a + c and to b = (a+c)/2 — three equivalent statements of the same condition.
- Q14Hard
The sum of first n terms of two APs are in ratio (3n + 8) : (7n + 15). Ratio of their 12th terms is:
A.12 : 25B.3 : 7C.8 : 15D.7 : 16✓ CorrectAnswer: D. 7 : 16
Explanation: For ratio of sums (3n+8):(7n+15), the mth-term ratio equals this expression at n = 2m − 1. For m = 12, n = 23: (3×23+8):(7×23+15) = 77:176 = 7:16.
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Start this chapter free →Arithmetic Progressions — FAQs
What are the key concepts in Class 10 Mathematics Arithmetic Progressions?+
An arithmetic progression is a list in which each term differs from the previous one by a fixed amount. This chapter finds any term directly, sums the first n terms, and applies both to problems about instalments, savings and patterns. Key ideas include Arithmetic progression (AP), Common difference (d), First term (a), General (nth) term.
What does Class 10 Mathematics Chapter 5 (Arithmetic Progressions) cover on XamBaaz?+
It has 90 NCERT-based MCQs on "Arithmetic Progressions": 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 Board exams and the JEE & NEET foundation years.
Are these "Arithmetic Progressions" questions free to practise?+
Yes. Sign in with Google to practise "Arithmetic Progressions" free. Full unlimited access is ₹999/year on a launch offer until 1 December 2026. No chapter is charged separately.
How should I revise "Arithmetic Progressions" 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 "Arithmetic 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 start practising, with instant scoring.
Is there negative marking in the "Arithmetic Progressions" quizzes?+
Yes. The timed quizzes use exam-style marking: +4 for a right answer, −1 for a wrong one and 0 for a skip. MHT-CET and CBSE board papers have no negative marking. Our mocks for those are scored their way.
What are the important questions from Arithmetic Progressions (Class 10 Mathematics)?+
The questions that matter most test Arithmetic progression (AP), Common difference (d), First term (a), General (nth) term. 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 Arithmetic Progressions?+
Yes — Class 10 Mathematics Arithmetic Progressions 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.