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Class 10 Arithmetic Progressions: 8 practice questions with answers, step by step
These are 8 practice questions on NCERT Class 10 Maths Chapter 5, Arithmetic Progressions, each with a worked answer. They cover what the chapter asks: finding the common difference, the nth term, which term of a list equals a given number, and the sum of the first n terms. Try each one on paper before you open the answer.
These questions are our own, drafted with AI help. Every answer was re-computed by a test script, but no practising teacher has reviewed them yet. If you find a mistake, please tell us.
What the chapter says you need
Four facts from the NCERT textbook (Mathematics, Textbook for Class X, Reprint 2026-27, Chapter 5, printed pages 49 to 72) cover every question below:
- An arithmetic progression (AP) is a list of numbers in which each term is obtained by adding a fixed number to the one before it. That fixed number is the common difference, d, and it can be positive, negative or zero (section 5.2, page 51).
- The nth term of an AP with first term a and common difference d is aₙ = a + (n − 1)d (section 5.3, page 57).
- The sum of the first n terms is S = n/2 × [2a + (n − 1)d] (section 5.4, page 64).
- If you know the first term a and the last term l, the sum is S = n/2 × (a + l) (section 5.4, page 64). The chapter summary repeats these results (section 5.5, page 72).
The nth term
Question 1. Find the 20th term of the AP 7, 11, 15, ...
Answer: Here a = 7 and d = 11 − 7 = 4. a₂₀ = a + 19d = 7 + 76 = 83.
Question 2. Which term of the AP 5, 9, 13, ... is 81?
Answer: Here a = 5 and d = 4. Put a + (n − 1)d = 81: 5 + (n − 1) × 4 = 81, so (n − 1) × 4 = 76, n − 1 = 19 and n = 20. So 81 is the 20th term.
Question 3. Is 301 a term of the AP 3, 7, 11, ...?
Answer: Here a = 3 and d = 4. If 301 were the nth term, then 3 + (n − 1) × 4 = 301, so (n − 1) × 4 = 298 and n − 1 = 74.5. The position n has to be a whole number, and n = 75.5 is not, so no, 301 is not a term of this AP.
Question 4. Find the common difference of the AP 10, 7, 4, ... and write the next two terms.
Answer: d = 7 − 10 = −3 (it can be negative). The next terms are 4 − 3 = 1 and 1 − 3 = −2. Check that the difference is the same each time: 4 − 7 = −3 and 1 − 4 = −3.
The sum of n terms
Question 5. Add up the first 15 terms of the AP 3, 5, 7, ... What is the total?
Answer: Here a = 3, d = 2 and n = 15. S = 15/2 × (2 × 3 + 14 × 2) = 15/2 × 34 = 255.
Question 6. Add up the first 20 terms of the AP 5, 9, 13, ... What is the total?
Answer: Here a = 5, d = 4 and n = 20. S = 20/2 × [2 × 5 + 19 × 4] = 10 × 86 = 860.
Question 7. An AP has first term 2, last term 50 and 25 terms. Find the sum of all its terms.
Answer: When the first and last terms are known, S = n/2 × (a + l) = 25/2 × (2 + 50) = 25 × 26 = 650. (The AP is 2, 4, 6, ..., 50, with common difference 2, and 25 terms.)
A word problem
Question 8. Meena saves ₹20 on the first day of a plan. Each day after that she saves ₹5 more than the day before. How much has she saved in all after 10 days?
Answer: The daily savings 20, 25, 30, ... form an AP with a = 20 and d = 5. For n = 10: S = 10/2 × (2 × 20 + 9 × 5) = 5 × 85 = ₹425. Check: the 10th day she saves 20 + 9 × 5 = ₹65, and 10/2 × (20 + 65) = 425.
Practise more, and check your marks
- Free practice, marked instantly in your browser: Class 10 Arithmetic Progressions questions. Questions 1, 2, 5 and 6 above are in this set.
- Printable worksheets with answer keys, in English, Hindi and Marathi: Class 10 worksheets.
- See how CBSE splits the 80 theory marks, and which unit Arithmetic Progressions belongs to, in our Class 10 Maths syllabus 2026-27 guide.
- The same step-by-step style for another chapter: Class 10 Quadratic Equations, 8 practice questions.
If you use an AI chatbot to check a solution, test its answer first, as in our guide to checking an AI's maths answers.
Where CMDLearn fits
CMDLearn is building an AI tutor for Classes 1 to 10 that explains a step and checks the child's working, but leaves the writing to the child. It is still in development, and no child uses it yet. If you would like to hear when there is something to try, you can join the waitlist.
Sources
All opened and read on 21 October 2026. Page numbers are the printed page numbers of the textbook.
- NCERT, Mathematics, Textbook for Class X, Chapter 5 "Arithmetic Progressions" (Reprint 2026-27), printed pages 49-72 (definition and common difference, section 5.2, page 51; the nth term, section 5.3, page 57; the sum of the first n terms and the form with the last term, section 5.4, page 64; summary, section 5.5, page 72): ncert.nic.in/textbook/pdf/jemh105.pdf
The definitions and formulas are from the textbook pages above. The questions, worked answers and checks are our own, and every number was re-computed by script. This guide is general information; follow your teacher and the official CBSE notices.