CBSE Class 10 Mathematics (Basic) Chapter 5 Arithmetic Progressions Important Questions 2027
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26 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 3.7 questions per paper (OR alternatives counted separately)
- 4 question patterns repeated across papers
Important topics in Arithmetic Progressions
| # | Topic | Asked in | Importance |
|---|---|---|---|
| 1 | Sum of first n terms of an AP | Board 2022Board 2023Board 2024Board 2025Board 2026Sample 2025Sample 2026 | ★★★☆☆ |
| 2 | nth term of an AP | Board 2022Board 2023Board 2024Board 2025Board 2026Sample 2025Sample 2026 | ★★☆☆☆ |
| 3 | Identifying AP / common difference | Board 2022Sample 2025Sample 2026 | ★☆☆☆☆ |
Repeated questions from Arithmetic Progressions
1. Find n from a target sum (solve quadratic)
5×Board 2022Board 2023Board 2024Board 2025Board 20262/5 marks
[Case: Saplings form a spiral of successive semicircles with centres alternately at A and B, starting at A, of radii 50 cm, 100 cm, 150 cm, ...; Spiral 1 has 10 flowers, Spiral 2 has 20, Spiral 3 has 30, and so on.] Till which spiral, will there be a total of 450 saplings ?
2. Find a specific nth term given a and d
5×Board 2022Board 2023Board 2025Board 20261/2 marks
[Case: Saplings form a spiral of successive semicircles with centres alternately at A and B, starting at A, of radii 50 cm, 100 cm, 150 cm, ...; Spiral 1 has 10 flowers, Spiral 2 has 20, Spiral 3 has 30, and so on.] What is the radius of the 13th spiral ?
3. Compute sum of first n terms of an AP
4×Board 2022Board 2023Board 2025Board 20262 marks
[Case: Saplings form a spiral of successive semicircles with centres alternately at A and B, starting at A, of radii 50 cm, 100 cm, 150 cm, ...; Spiral 1 has 10 flowers, Spiral 2 has 20, Spiral 3 has 30, and so on.] Find the total number of saplings till the 11th spiral.
4. Find n given the value of the nth term
2×Board 2025Board 20261 marks
[Case: Saplings form a spiral of successive semicircles with centres alternately at A and B, starting at A, of radii 50 cm, 100 cm, 150 cm, ...; Spiral 1 has 10 flowers, Spiral 2 has 20, Spiral 3 has 30, and so on.] If the radius of the nth spiral is 500 cm, find the value of n.
Arithmetic Progressions questions by paper
| Paper | Questions | Marks |
|---|---|---|
| Board 2022 | 4 | 8 |
| Board 2023 | 5 | 7 |
| Board 2024 | 2 | 6 |
| Board 2025 | 4 | 6 |
| Sample 2025 | 4 | 6 |
| Board 2026 | 4 | 6 |
| Sample 2026 | 3 | 5 |
Counts include both options of internal-choice (OR) questions.
Previous year questions: Arithmetic Progressions
Board 2026 4 questions
[Case: Saplings form a spiral of successive semicircles with centres alternately at A and B, starting at A, of radii 50 cm, 100 cm, 150 cm, ...; Spiral 1 has 10 flowers, Spiral 2 has 20, Spiral 3 has 30, and so on.] What is the radius of the 13th spiral ?
[Case: Saplings form a spiral of successive semicircles with centres alternately at A and B, starting at A, of radii 50 cm, 100 cm, 150 cm, ...; Spiral 1 has 10 flowers, Spiral 2 has 20, Spiral 3 has 30, and so on.] If the radius of the nth spiral is 500 cm, find the value of n.
[Case: Saplings form a spiral of successive semicircles with centres alternately at A and B, starting at A, of radii 50 cm, 100 cm, 150 cm, ...; Spiral 1 has 10 flowers, Spiral 2 has 20, Spiral 3 has 30, and so on.] Find the total number of saplings till the 11th spiral.
[Case: Saplings form a spiral of successive semicircles with centres alternately at A and B, starting at A, of radii 50 cm, 100 cm, 150 cm, ...; Spiral 1 has 10 flowers, Spiral 2 has 20, Spiral 3 has 30, and so on.] Till which spiral, will there be a total of 450 saplings ?
Sample 2026 3 questions
The value of x for which 2x, (x + 10) and (3x + 2) are the three consecutive terms of an AP is
A) 6
B) −6
C) −2
D) 2
If 1 + 2 + 3 + 4 + ⋯ + 50 = 25k, then k =
A) 50
B) 51
C) 49
D) 26
The sum of first n terms of an AP is 5n2 − n. Find the nth term of the AP.
Board 2025 4 questions
[Case context: A spiral of successive semicircles with centres alternately at A and B has radii 50 cm, 100 cm, 150 cm, ...; Spiral 1 has 10 flowers, Spiral 2 has 20, Spiral 3 has 30, and so on.] What is the radius of the 13th spiral ?
[Case context: A spiral of semicircles with radii 50 cm, 100 cm, 150 cm, ...] If the radius of the nth spiral is 500 cm, find the value of n.
[Case context: Spiral 1 has 10 flowers, Spiral 2 has 20, Spiral 3 has 30, and so on.] Find the total number of saplings till the 11th spiral.
[Case context: Spiral 1 has 10 flowers, Spiral 2 has 20, Spiral 3 has 30, and so on.] Till which spiral, will there be a total of 450 saplings ?
Sample 2025 4 questions
The 4th term from the end of the A.P. −8, −5, −2, ..., 49 is (A) 37 (B) 40 (C) 1 (D) 43
Assertion (A): The sequence −1, −1−1, ..., −1 is an AP. Reason (R): In an AP, an − an−1 is constant where n ≥ 2 and n ∈ N.
The sum of the first 12 terms of an A.P. is 900. If its first term is 20 then find the common difference and 12th term.
The sum of first n terms of an A.P. is represented by Sn = 6n − n2. Find the common difference.
Board 2024 2 questions
In an A.P., if a = 8 and a10 = -19, then value of d is : (a) 3 (b) -11/9 (c) -27/10 (d) -3
How many terms of the A.P. 27, 24, 21, ... must be taken so that their sum is 105 ? Which term of the A.P. is zero ?
Board 2023 5 questions
The seventh term of an A.P. whose first term is 28 and common difference − 4, is : (a) 0 (b) 4 (c) 52 (d) 56
[Case: Aahana places pots in rows — 2 in the first row, 5 in the second, 8 in the third, and so on.] Find the number of pots placed in the 10th row.
[Case: Aahana places pots in rows — 2 in the first row, 5 in the second, 8 in the third, and so on.] Find the difference in the number of pots placed in 5th row and 2nd row.
[Case: Aahana places pots in rows — 2 in the first row, 5 in the second, 8 in the third, and so on.] If Aahana wants to place 100 pots in total, then find the total number of rows formed in the arrangement.
[Case: Aahana places pots in rows — 2 in the first row, 5 in the second, 8 in the third, and so on.] If Aahana has sufficient space for 12 rows, then how many total number of pots are placed by her with the same arrangement ?
Board 2022 4 questions
In an AP, if a = 50, d = -4 and Sn = 0, then find the value of n.
Find the sum of the first twelve 2-digit multiples of 7, using an AP.
[Case context: A footmat (rug) is made out of old t-shirts yarn; the number of stitches in circular rows makes the pattern 6, 12, 18, 24, ...] Check whether the given pattern forms an AP. If yes, find the common difference and the next term of the AP.
[Case context: A footmat (rug) is made out of old t-shirts yarn; the number of stitches in circular rows makes the pattern 6, 12, 18, 24, ...] Write the nth term of the AP. Hence, find the number of stitches in the 10th circular row.
Frequently asked questions
What are the most important topics in CBSE Class 10 Mathematics (Basic) Chapter 5 Arithmetic Progressions?
By how often and how recently they were asked: Sum of first n terms of an AP; nth term of an AP; Identifying AP / common difference.
How many marks does Arithmetic Progressions carry in the CBSE Class 10 Mathematics (Basic) exam?
Arithmetic Progressions is part of the Algebra unit, which carries 20 marks in the official syllabus. In the analysed papers it had about 3.7 questions per paper.
Do questions from Arithmetic Progressions repeat in board exams?
Yes — 4 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.