CBSE Class 10 Mathematics 2026 - Chapter 5 Arithmetic Progressions

THE GOAL

CHAPTER 5 : ARITHMETIC PROGRESSIONS

CBSE Class 10 Mathematics — PYQs 2026 | Basic + Standard

BASIC QUESTION PAPER 2026

SECTION A : CASE STUDY BASED QUESTIONS (4 Marks Each)

Type A : Spiral Pattern — Rose Saplings

1. Saplings of rose flowers are planted in a garden to form a spiral pattern made of successive semicircles with alternating centres A and B. The radii of the successive spirals are 50 cm, 100 cm, 150 cm, .... Spiral 1 has 10 flowers, Spiral 2 has 20 flowers, Spiral 3 has 30 flowers, and so on.

(i) [1 Mark] What is the radius of the 13^th spiral?

(ii) [1 Mark] If the radius of the n^th spiral is 500 cm, find the value of n.

(iii) [2 Marks]

(a) Find the total number of saplings till the 11^th spiral.

(b) Till which spiral will there be a total of 450 saplings?

[Set 430/1/1 Q37; Set 430/1/2 Q36; Set 430/1/3 Q38]

Type B : Loan Repayment — Monthly Instalments

2. A woman borrowed ₹10,00,000 and promised to return it in monthly instalments. She paid ₹10,000 in the first month, ₹15,000 in the second month, ₹20,000 in the third month, and so on, increasing the instalment uniformly.

(i) [1 Mark] Find the amount of instalment paid in the tenth month.

(ii) [1 Mark] In which instalment did she pay ₹40,000?

(iii) [2 Marks]

(a) If she returned ₹11,50,000 in all, how many instalments did she pay?

(b) By which instalment has she returned a total amount of ₹3,25,000?

[Set 430/2/1 Q37; Set 430/2/2 Q36; Set 430/2/3 Q38]

Type C : Yoga Sessions — Increasing Participants

3. Yoga sessions are held daily in a society park. On day one, 5 people joined. Every next day, 3 more people kept joining. Thus, Day 2 had 8 people, Day 3 had 11 people, and so on.

(i) [1 Mark] On which day did 59 people join the yoga session?

(ii) [1 Mark] How many people joined the yoga session on the 31^st day?

(iii) [2 Marks]

(a) The yoga instructor was paid ₹100 for each person attending. On which day would he earn ₹5,000?

(b) What was the total amount earned by the yoga instructor in 16 days?

[Set 430/3/1 Q36; Set 430/3/2 Q38; Set 430/3/3 Q37]

STANDARD QUESTION PAPER 2026

SECTION A : MULTIPLE CHOICE QUESTIONS (1 Mark Each)

A. Finding Terms and Common Differences

1. The common difference of the A.P. √2, 2√2, 3√2, 4√2, ... is:

(A) √2 (B) 1 (C) 2√2 (D) −√2

[Set 30/1/1 Q6; Set 30/1/3 Q4]

2. The nth term of an A.P. is 2n + 1. Its common difference is:

(A) 2 (B) 2n (C) 1 (D) 2n + 1

[Set 30/4/1 Q3]

3. In an A.P., if a₁₄ − a₈ = 24, then the common difference of the A.P. is:

(A) 6 (B) 4 (C) ±4 (D) 3

[Set 30/5/2 Q3]

4. The first term of an A.P. is p and the common difference is q. Then its 10th term is:

(A) q − 9p (B) p − 9q (C) p + 9q (D) 2p + 9q

[Set 30/1/2 Q7]

5. If a_n represents the nth term of the A.P. −15/4, −10/4, −5/4, ..., then the value of a₁₆ − a₁₂ is:

(A) 4 (B) 5/4 (C) 5 (D) 25/4

[Set 30/5/1 Q8; Set 30/5/3 Q2]

6. The nth term of the A.P. −1/3, 2/3, 5/3, 8/3, ... is:

(A) 3n − 4 (B) n − 4/3 (C) (n − 2)/3 (D) (n − 4)/3

[Set 30/3/1 Q11; Set 30/3/2 Q13; Set 30/3/3 Q15]

B. Identifying Arithmetic Progressions

7. Which of the following sequences is NOT an A.P.?

(A) 2, 5/2, 3, 7/2, ...
(B) −1.2, −3.2, −5.2, −7.2, ...
(C) √2, √8, √18, ...
(D) 1², 3², 5², 7², ...

[Set 30/2/1 Q7; Set 30/2/3 Q14]

C. Solving for Variables

8. The value of x for which 2x, (x + 10) and (3x + 2) are the three consecutive terms of an A.P. is:

(A) 6 (B) −6 (C) 18 (D) −18

[Set 30/2/2 Q5]

D. Counting Multiples and Sums

9. The number of multiples of 4 lying between 12 and 250 is:

(A) 59 (B) 59.5 (C) 60 (D) 61

[Set 30/3/1 Q6; Set 30/3/2 Q10]

10. The number of multiples of 6 lying between 25 and 363 is:

(A) 56 (B) 56.5 (C) 57 (D) 58

[Set 30/3/3 Q1]

11. If the sum of the first ten terms of an A.P. is zero, with a as the first term and d as the common difference, which of the following relation is true?

(A) 10a + 9d = 0
(B) 2a = 9d
(C) a₁₀ = −a
(D) a₁₀ = a

[Set 30/4/3 Q16]

12. In an A.P., a = −3 and S₁₇ = 357. The value of a₁₇ is:

(A) 47 (B) 39 (C) 45 (D) 42

[Set 30/4/2 Q17]

SECTION B : VERY SHORT ANSWER QUESTIONS (2 Marks Each)

13. In an A.P., the first term is 32 and the last term is −10. If the common difference is −2, find the number of terms and their sum.

[Set 30/3/1 Q22(a)]

14. Find the sum of the first 28 terms of an A.P. whose nth term is given by

a_n = 3n − 2

[Set 30/3/1 Q22(b)]

SECTION C : SHORT ANSWER QUESTIONS (3 Marks Each)

A. Forming and Analyzing A.P.s

15. In an A.P., the 15th term exceeds the 8th term by 21. If the sum of the first 10 terms is 55, then form the A.P.

[Set 30/5/1 Q27(a); Set 30/5/2 Q29(a); Set 30/5/3 Q28(a)]

16. The sum of the first n terms of an A.P. is

S_n = 2n² + 13n.

Find its nth term and hence find the 10th term.

[Set 30/5/1 Q27(b); Set 30/5/2 Q29(b); Set 30/5/3 Q28(b)]

17. In an A.P. the first term is 4 and the last term is 31. If the sum of all terms is 175, find the number of terms and the common difference.

[Set 30/3/3 Q23(a)]

18. How many terms of the A.P. 21, 18, 15, ... must be added to get the sum zero?

[Set 30/3/3 Q23(b)]

SECTION D : CASE STUDY BASED QUESTIONS (4 Marks Each)

Type A : The 'Kolam' Art — Dots in Squares

19. Kolam is drawn on a grid pattern of dots. There are 4 dots in the first square, 8 dots in the second square, 12 dots in the third square, and so on.

(i) [1 Mark] Show that the number of dots forms an A.P. Write its first term and common difference.

(ii) [1 Mark] Write the nth term of the A.P. formed.

(iii) [2 Marks]

(a) If a total of 220 dots are used, find the number of squares formed.

(b) Is it possible to complete n squares using 100 dots? If yes, find n.

[Set 30/4/1 Q37; Set 30/4/2 Q36; Set 30/4/3 Q36]

Type B : The Potato Race

20. A bucket is placed at the starting point, which is 5 m from the first potato. The other potatoes are arranged 3 m apart in a straight line, with a total of 10 potatoes.

(i) [1 Mark] What is the distance covered to pick up the first potato and drop it in the bucket?

(ii) [1 Mark] What is the distance covered to pick up the second potato and drop it in the bucket?

(iii) [2 Marks]

(a) What is the total distance the competitor has to run?

(b) If the average speed is 5 m/s, find the time taken to collect all the potatoes.

[Set 30/1/1 Q36]

Type C : Elder Brother's Loan Repayment

21. Your elder brother repays his total loan of ₹1,18,000 by paying every month, starting with the first instalment of ₹1,000. He increases the instalment by ₹100 every month.

(i) [1 Mark] Find the amount paid by him in the 30th instalment.

(ii) [1 Mark] If the total number of instalments is 40, find the amount paid in the last instalment.

(iii) [2 Marks]

(a) What amount does he still have to pay after the 30th instalment?

(b) Find the ratio of the tenth instalment to the last instalment.

[Set 30/2/1 Q36; Set 30/2/2 Q38; Set 30/2/3 Q37]