CBSE Class 10 Mathematics (Standard) Chapter 5 Arithmetic Progressions Important Questions 2027
Last updated:
32 questions from Arithmetic Progressions appeared in 7 of the 7 CBSE papers we analysed (2022–2026) — here are the topics that matter, the questions that repeat, and every previous-year question from this chapter.
Key facts
- Algebra unit — 20 marks in the official syllabus
- Asked in 7 of 7 analysed papers (2022–2026)
- About 4.6 questions per paper (OR alternatives counted separately)
- 3 question patterns repeated across papers
Important topics in Arithmetic Progressions
| # | Topic | Asked in | Importance |
|---|---|---|---|
| 1 | nth term of an AP | Board 2022Board 2023Board 2025Board 2026Sample 2025Sample 2026 | ★★★★☆ |
| 2 | Sum of first n terms of an AP | Board 2022Board 2024Board 2025Board 2026Sample 2025Sample 2026 | ★★★★☆ |
| 3 | Identifying AP / common difference | Board 2023Board 2026Sample 2025Sample 2026 | ★★☆☆☆ |
| 4 | Word problems on AP | Board 2022Board 2023 | ★☆☆☆☆ |
Repeated questions from Arithmetic Progressions
1. Direct an computation in a real-life context
5×Board 2025Board 2026Sample 20261 marks
[case context: elder brother repays a bank loan of Rs 1,18,000 in monthly instalments starting at Rs 1,000 and increasing by Rs 100 every month (an AP)] Find the amount paid by him in the 30th instalment.
2. Direct Sn given first term and common difference
5×Board 2022Board 2025Sample 2025Sample 20262 marks
[case context: Teacher asks students to write examples of A.P.; Aryan writes -5, -2, 1, 4, ... and Roshan writes 187, 184, 181, ...] Find the sum of first 10 terms of the progression written by Aryan.
3. Recover terms from polynomial Sn
2×Board 2022Board 20251/2 marks
If the sum of first m terms of an AP is 2m2 + 3m, then its second term is : (A) 10 (B) 9 (C) 12 (D) 4
Arithmetic Progressions questions by paper
| Paper | Questions | Marks |
|---|---|---|
| Board 2022 | 4 | 8 |
| Board 2023 | 3 | 11 |
| Board 2024 | 3 | 11 |
| Board 2025 | 5 | 7 |
| Sample 2025 | 5 | 7 |
| Board 2026 | 6 | 8 |
| Sample 2026 | 6 | 10 |
Counts include both options of internal-choice (OR) questions.
Previous year questions: Arithmetic Progressions
Board 2026 6 questions
Which of the following sequence is not an A.P. ? (A) 2, 5/2, 3, 7/2, ... (B) -1.2, -3.2, -5.2, -7.2, ... (C) sqrt(2), sqrt(8), sqrt(18), ... (D) 12, 32, 52, 72, ...
Assertion (A) : The mean of first 'n' natural numbers is (n - 1)/2. Reason (R) : The sum of first 'n' natural numbers is n(n + 1)/2. [Choose: both true R explains A / both true R does not explain A / A true R false / A false R true]
[case context: elder brother repays a bank loan of Rs 1,18,000 in monthly instalments starting at Rs 1,000 and increasing by Rs 100 every month (an AP)] Find the amount paid by him in the 30th instalment.
[case context: elder brother repays a bank loan of Rs 1,18,000 in monthly instalments starting at Rs 1,000 and increasing by Rs 100 every month (an AP)] If the total number of instalments is 40, what is the amount paid in the last instalment ?
[case context: elder brother repays a bank loan of Rs 1,18,000 in monthly instalments starting at Rs 1,000 and increasing by Rs 100 every month (an AP)] What amount does he still have to pay after the 30th instalment ?
[case context: elder brother repays a bank loan of Rs 1,18,000 in monthly instalments starting at Rs 1,000 and increasing by Rs 100 every month (an AP)] Find the ratio of the tenth instalment to the last instalment.
Sample 2026 6 questions
[case context: Teacher asks students to write examples of A.P.; Aryan writes -5, -2, 1, 4, ... and Roshan writes 187, 184, 181, ...] Find the sum of the common difference of the two progressions.
[case context: Teacher asks students to write examples of A.P.; Aryan writes -5, -2, 1, 4, ... and Roshan writes 187, 184, 181, ...] Find the 34th term of the progression written by Roshan.
The A.P. 8, 10, 12, ....... has 60 terms. Find the sum of last 10 terms.
Find the middle term of A.P. 6, 13, 20, ......, 230
[case context: Teacher asks students to write examples of A.P.; Aryan writes -5, -2, 1, 4, ... and Roshan writes 187, 184, 181, ...] Find the sum of first 10 terms of the progression written by Aryan.
[case context: Teacher asks students to write examples of A.P.; Aryan writes -5, -2, 1, 4, ... and Roshan writes 187, 184, 181, ...] Which term of the progressions will have the same value?
Board 2025 5 questions
If the sum of first m terms of an AP is 2m2 + 3m, then its second term is : (A) 10 (B) 9 (C) 12 (D) 4
[case context: charity run with rounds of 300 m increasing by 50 m each subsequent round, 10 rounds total, forming an AP] Write the fourth, fifth and sixth term of the Arithmetic Progression so formed.
[case context: charity run with rounds of 300 m increasing by 50 m each subsequent round, 10 rounds total, forming an AP] Determine the distance of the 8th round.
[case context: charity run with rounds of 300 m increasing by 50 m each subsequent round, 10 rounds total, forming an AP] Find the total distance run after completing all 10 rounds.
[case context: charity run with rounds of 300 m increasing by 50 m each subsequent round, 10 rounds total, forming an AP] If a runner completes only the first 6 rounds, what is the total distance run by the runner ?
Sample 2025 5 questions
If nth term of an A.P. is 7n-4 then the common difference of the A.P. is A) 7 B) 7n C) -4 D) 4
[case context] Glass jars in a store are stacked in layers: 3 jars in top layer, 6 in next, 9 in 3rd layer and so on till the 8th layer. (i) Write an A.P whose terms represent the number of jars in different layers starting from top. Also, find the common difference.
[case context] Glass jars stacked in layers forming AP 3, 6, 9, ... up to 8th layer. (ii) Is it possible to arrange 34 jars in a layer if this pattern is continued? Justify your answer.
[case context] Glass jars stacked in layers forming AP 3, 6, 9, ... (iii)(A) If there are 'n' number of rows in a layer then find the expression for finding the total number of jars in terms of n. Hence find S8.
[case context] Glass jars stacked in layers forming AP 3, 6, 9, ... (iii)(B) The shopkeeper added 3 jars in each layer. How many jars are there in the 5th layer from the top?
Board 2024 3 questions
In an A.P., if the first term a = 7, nth term an = 84 and the sum of first n terms sn = 2093/2, then n is equal to: (a) 22 (b) 24 (c) 23 (d) 26
The sum of first and eighth terms of an A.P. is 32 and their product is 60. Find the first term and common difference of the A.P. Hence, also find the sum of its first 20 terms.
In an A.P. of 40 terms, the sum of first 9 terms is 153 and the sum of last 6 terms is 687. Determine the first term and common difference of A.P. Also, find the sum of all the terms of the A.P.
Board 2023 3 questions
If p - 1, p + 1 and 2p + 3 are in A.P., then the value of p is (A) -2 (B) 4 (C) 0 (D) 2
The ratio of the 11th term to 17th term of an A.P. is 3 : 4. Find the ratio of 5th term to 21st term of the same A.P. Also, find the ratio of the sum of first 5 terms to that of first 21 terms.
250 logs are stacked in the following manner: 22 logs in the bottom row, 21 in the next row, 20 in the row next to it and so on (as shown by an example). In how many rows, are the 250 logs placed and how many logs are there in the top row?
Board 2022 4 questions
Find the sum of first 30 terms of AP : -30, -24, -18, ..... .
In an AP if Sn = n(4n + 1), then find the AP.
[case context: matchstick patterns based on linear relations; figures 1, 2, 3 made of matchstick triangles and squares form an AP] Write the AP for the number of triangles used in the figures. Also, write the nth term of this AP.
[case context: matchstick patterns based on linear relations; figures 1, 2, 3 made of matchstick triangles and squares form an AP] Which figure has 61 matchsticks?
Frequently asked questions
What are the most important topics in CBSE Class 10 Mathematics (Standard) Chapter 5 Arithmetic Progressions?
By how often and how recently they were asked: nth term of an AP; Sum of first n terms of an AP; Identifying AP / common difference.
How many marks does Arithmetic Progressions carry in the CBSE Class 10 Mathematics (Standard) exam?
Arithmetic Progressions is part of the Algebra unit, which carries 20 marks in the official syllabus. In the analysed papers it had about 4.6 questions per paper.
Do questions from Arithmetic Progressions repeat in board exams?
Yes — 3 question patterns from this chapter appeared in two or more past board or official sample papers. They are listed on this page with the years they were asked.