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Class 10 Maths Chapter 5: Arithmetic Progressions — Important Questions & Sample Paper

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Reviewed by qpaper's CBSE curriculum team · Edited by Mohit · Updated June 2026

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Yes — this page has 44+ original Class 10 Mathematics Chapter 5 (“Arithmetic Progressions”) important questions with answers (Multiple Choice (MCQ), Assertion–Reason, Short Answer, Short Answer, Long Answer, Case Study). Practise them free, or generate a full CBSE board-pattern sample paper (80 marks) and export it to PDF or Word — in English & Hindi, for 2026-27.

Class 10 Mathematics Chapter 5, Arithmetic Progressions, introduces one of the fundamental concepts in algebra: sequences where the difference between consecutive terms is constant. This chapter equips students with the ability to identify, formulate, and solve problems involving APs, which are not only essential for higher mathematics but also appear in real-life situations like calculating loan instalments or predicting patterns. Key topics include understanding the first term (a) and common difference (d), deriving the nth term (an = a + (n-1)d) and the sum of the first n terms (Sn = n/2[2a + (n-1)d]). Students learn to apply these formulas to find missing terms, determine the number of terms, and compute sums. CBSE exam questions typically test both direct formula application and complex, multi-step problems. For instance, finding specific terms (e.g., 15th term of an AP), determining an AP when terms or sums satisfy certain conditions, and solving word problems like a person repaying a loan in monthly instalments forming an AP. Other common question types involve ratios of terms or sums, and selecting terms to form an AP under given sum and product constraints. Practising these variations helps students master the logical reasoning required to excel in the chapter. On qpaper.in, teachers can generate custom question papers covering all these aspects to prepare students thoroughly.

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Mathematics — Arithmetic Progressions

Class 10Time: 3 hrsMax Marks: 80

SECTION A

  1. 1.

    In an arithmetic progression with 60 terms, the sum of the first 20 terms is 210 and the sum of the first 30 terms is 465. What is the sum of the last 10 terms?

    (a) 555(b) 500(c) 510(d) 525
    1
  2. 2.

    If the sum of the first p terms of an arithmetic progression is q and the sum of the first q terms is p (p ≠ q), then the sum of its first (p+q) terms is:

    (a) p+q(b) 0(c) –(p+q)(d) 1
    1
  3. 3.

    For an arithmetic progression, the ratio of the sum of m terms to the sum of n terms is m² : n². The ratio of its mth term to its nth term is:

    (a) (2m+1):(2n+1)(b) (2m-1):(2n-1)(c) m:n(d) (m+1):(n+1)
    1

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Marks distribution & blueprint

In a CBSE exam, this chapter typically contributes questions across the following types. The last column shows how many original questions of each type we have ready in our bank for this chapter:

Question typeMarks eachIn our bank
Multiple Choice (MCQ)1 mark13
Assertion–Reason1 mark6
Short Answer2 marks8
Short Answer3 marks6
Long Answer5 marks5
Case Study4 marks6

44 original, exam-style questions in our bank for this chapter — with answers.

Important & sample questions (with answers)

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  1. Q1. In an arithmetic progression with 60 terms, the sum of the first 20 terms is 210 and the sum of the first 30 terms is 465. What is the sum of the last 10 terms?

    1 mark
    Multiple Choice (MCQ)
    (A) 555(B) 500(C) 510(D) 525
    ▸ Answer

    555

  2. Q2. If the sum of the first p terms of an arithmetic progression is q and the sum of the first q terms is p (p ≠ q), then the sum of its first (p+q) terms is:

    1 mark
    Multiple Choice (MCQ)
    (A) p+q(B) 0(C) –(p+q)(D) 1
    ▸ Answer

    –(p+q)

  3. Q3. For an arithmetic progression, the ratio of the sum of m terms to the sum of n terms is m² : n². The ratio of its mth term to its nth term is:

    1 mark
    Multiple Choice (MCQ)
    (A) (2m+1):(2n+1)(B) (2m-1):(2n-1)(C) m:n(D) (m+1):(n+1)
    ▸ Answer

    (2m-1):(2n-1)

  4. Q4. Which term of the arithmetic progression 21, 18, 15, ... becomes zero?

    1 mark
    Multiple Choice (MCQ)
    (A) 7th(B) 8th(C) 9th(D) 10th
    ▸ Answer

    8th

  5. Q5. Assertion (A): In an AP, if the mth term is 1/n and the nth term is 1/m (m ≠ n), then the mnth term is 1. Reason (R): From the given conditions, we obtain common difference d = 1/(mn) and first term a = 1/(mn), so the mnth term comes out to be 1.

    1 mark
    Assertion–Reason
    (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.
    ▸ Answer

    Both A and R are true and R is the correct explanation of A.

  6. Q6. The sum of the first p terms of an AP is q, and the sum of the first q terms is p. Find the sum of the first (p+q) terms.

    2 marks
    Short Answer
    ▸ Answer

    - (p + q)

  7. Q7. If the 4th term of an AP is 15 and the 9th term is 30, find the common difference.

    2 marks
    Short Answer
    ▸ Answer

    3

  8. Q8. Write the next two terms of the arithmetic progression: √2, √8, √18, √32, …

    3 marks
    Short Answer
    ▸ Answer

    √50, √72

  9. Q9. If the sum of the first n terms of an AP is given by S_n = 5n - n², find the 10th term.

    3 marks
    Short Answer
    ▸ Answer

    -14

  10. Q10. Find four numbers in arithmetic progression whose sum is 40. The ratio of the product of the first and fourth numbers to the product of the second and third numbers is 19 : 91.

    5 marks
    Long Answer
    ▸ Answer

    1, 7, 13, 19

  11. Q11. The sum of the first n terms of an arithmetic progression is given by S_n = 4n^2 – 2n. Find the progression and its 25th term.

    5 marks
    Long Answer
    ▸ Answer

    AP: 2, 10, 18, … ; 25th term = 194

  12. Q12. A staircase has a total of 25 steps. The thickness (height) of the first step is 10 cm, and each subsequent step is 2 cm thicker than the previous one. The steps are placed one on top of another to build the staircase.

    4 marks
    Case Study
    1. (i) Find the height of the 25th step.1 mark
    2. (ii) What is the total vertical height of the staircase from the ground to the top of the last step?2 marks
    3. (iii) A person wants to stand at a height of exactly 400 cm above the ground on this staircase. On which step should he stand?1 mark
    ▸ Answer

    (i) 58 cm, (ii) 850 cm, (iii) 16th step

Frequently asked questions

What is the formula for the nth term of an Arithmetic Progression?

The nth term of an AP is given by an = a + (n-1)d, where a is the first term, d is the common difference, and n is the term number.

How do I solve problems involving the sum of an AP when the first and last terms are known?

If you know the first term a, the last term l, and the number of terms n, the sum Sn = n/2 (a + l). This is a direct formula, provided all three values are known.

What types of word problems frequently appear in CBSE Class 10 Arithmetic Progressions exams?

Common word problems include loan repayment in instalments forming an AP, finding numbers in AP under sum and product conditions, and ratio-based questions on terms or sums. These require setting up and solving equations using AP formulas.

How can I find the common difference if two terms of an AP are given?

Subtract the term with smaller index from the term with larger index, then divide by the difference in their positions: d = (am - an) / (m-n). For example, if the 3rd term is 12 and 7th is 24, d = (24-12)/(7-3) = 3.

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Class 10 Maths Ch5 — Important Questions & Sample Paper with Answers | Free PDF