CBSE Class 10 Mathematics Arithmetic Progressions Worksheet Set 01

Class 10 Mathematics Practice Set: Chapter 05 Arithmetic Progression

Access printable practice worksheets for Chapter 05 Arithmetic Progression designed to align with the 2026-27 academic syllabus for Class 10 Mathematics. These structured exercises help students evaluate their conceptual understanding and improve exam readiness.

Download Chapter 05 Arithmetic Progression Worksheet PDF

Access the complete worksheet PDF for Chapter 05 Arithmetic Progression below. Regular practice with these targeted questions builds familiarity with standard exam patterns and helps secure higher marks in final Mathematics evaluations.

Multiple Choice Questions 

Question. The sum of first five terms of the AP: 3, 7, 11, 15, ... is:
(a) 44
(b) 55
(c) 22
(d) 11
Answer : B

Question. If the first term of an AP is 1 and the common difference is 2, then the sum of first 26 terms is
(a) 484
(b) 576
(c) 676
(d) 625
Answer : C

Question. If the sum to n terms of an AP is 3n2 + 4n, then the common difference of the AP is
(a) 7
(b) 5
(c) 8
(d) 6
Answer : D

Question. If a, b, c are in AP then ab + bc =
(a) b
(b) b2
(c) 2b2
(d) 1/b
Answer : C

Question. The sum of all natural numbers which are less than 100 and divisible by 6 is
(a) 412
(b) 510
(c) 672
(d) 816
Answer : D

 

Assertion-Reason Type Questions

In the following questions, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice as:
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A).
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation ofassertion (A).
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.

Question. Assertion (A): Sum of the first 10 terms of the arithmetic progression –0.5, –1.0, –1.5,... is 27.5.
Reason (R): Sum of first n terms of an AP is given as Sn = n/2 [2a + (n – 1)d] where a = first term, d = common difference.
Answer : A

Question. Assertion (A): The sum of the first n terms of an AP is given by Sn = 3n2 – 4n. Then its nth term, an = 6n – 7.
Reason (R): nth term of an AP, whose sum of n terms is Sn, is given by an = Sn – Sn–1.
Answer : A

Question. Assertion (A): Sum of first hundred even natural numbers divisible by 5 is 500.
Reason (R): Sum of the first n terms of an AP is given by Sn = n/2 [a + l] where l = last term.
Answer : D

Case Study Based Questions

I. Pollution—A Major Problem: One of the major serious problems that the world is facing today is the environmental
pollution. Common types of pollution include light, noise, water and air pollution.

""CBSE-Class-10-Mathematics-Arithmetic-Progressions-Worksheet-Set-A

In a school, students thoughts of planting trees in and around the school to reduce noise pollution and air pollution.
Condition I: It was decided that the number of trees that each section of each class will plant be the same as the class in
which they are studying, e.g. a section of class I will plant 1 tree a section of class II will plant 2 trees and so on a section
of class XII will plant 12 trees.
Condition II: It was decided that the number of trees that each section of each class will plant be the double of the class
in which they are studying, e.g. a section of class I will plant 2 trees, a section of class II will plant 4 trees and so on a
section of class XII will plant 24 trees.

Refer to Condition I

Question. The AP formed by sequence i.e. number of plants by students is
(a) 0, 1, 2, 3, ..., 12
(b) 1, 2, 3, 4, ..., 12
(c) 0, 1, 2, 3, ..., 15
(d) 1, 2, 3, 4, ..., 15
Answer : B

Question. If there are two sections of each class, how many trees will be planted by the students?
(a) 126
(b) 152
(c) 156
(d) 184
Answer : C

Question. If there are three sections of each class, how many trees will be planted by the students?
(a) 234
(b) 260
(c) 310
(d) 326
Answer : A

Refer to Condition II

Question. If there are two sections of each class, how many trees will be planted by the students?
(a) 422
(b) 312
(c) 360
(d) 540
Answer : B

Question. If there are three sections of each class, how many trees will be planted by the students?
(a) 468
(b) 590
(c) 710
(d) 620
Answer : A
 

II. Your elder brother wants to buy a car and plans to take loan from a bank for his car. He repays his total loan of ₹ 1,18,000 by paying every month starting with the first instalment of ₹ 1000. If he increases the instalment by ₹ 100 every month, answer the following:

""CBSE-Class-10-Mathematics-Arithmetic-Progressions-Worksheet-Set-A-1

Question. The amount paid by him in 30th installment is
(a) ₹ 3900
(b) ₹ 3500
(c) ₹ 3700
(d) ₹ 3600
Answer : A

Question. The total amount paid by him upto 30 installments is
(a) ₹ 37000
(b) ₹ 73500
(c) ₹ 75300
(d) ₹ 75000
Answer : B

Question. What amount does he still have to pay after 30th installment?
(a) ₹ 45500
(b) ₹ 49000
(c) ₹ 44500
(d) ₹ 54000
Answer : C

Question. If total installments are 40, then amount paid in the last installment is
(a) ₹ 4900
(b) ₹ 3900
(c) ₹ 5900
(d) ₹ 9400
Answer : A

Question. The ratio of the 1st installment to the last installment is
(a) 1 : 49
(b) 10 : 49
(c) 10 : 39
(d) 39 : 10
Answer : B

 

 

ARITHMETIC PROGRESSIONS

Q.- Determine the general term of an A.P. whose 7th term is –1 and 16th term 17.
 
Sol. Let a be the first term and d be the common difference of the given A.P. Let the A.P. be a1, a2, a3, ....... an, .......
It is given that a7 = – 1 and a16 = 17
a + (7 – 1) d = – 1 and, a + (16 – 1) d = 17
=>  a + 6d = – 1                ....(i)
and, a + 15d = 17            ....(ii)
Subtracting equation (i) from equation (ii), we get
9d = 18
=>  d = 2
Putting d = 2 in equation (i), we get
a + 12 = – 1  
=> a = – 13
Now, General term = an
=>  a + (n – 1) d = – 13 + (n – 1) × 2 = 2n – 15
 
Q.-  If five times the fifth term of an A.P. is equal to 8 times its eight term, show that its 13th term is zero.
 
Sol. Let a1, a2, a3, ..... , an, .... be the A.P. with its first term = a and common difference = d.
It is given that 5a5 = 8a8
=> 5(a + 4d) = 8 (a + 7d)
=> 5a + 20d = 8a + 56d    => 3a + 36d = 0
=>3(a + 12d) = 0              => a + 12d = 0
=> a + (13 – 1) d = 0         => a13 = 0
 
Q.- If m times mth term of an A.P. is equal to n times its nth term, show that the (m + n) term of the A.P. is zero.
 
Sol. Let a be the first term and d be the common difference of the given A.P. Then, m times mth term = n times nth term
=> mam = nan
=> m{a + (m – 1) d} = n {a + (n – 1) d}
=> m{a + (m – 1) d} – n{a + (n – 1) d} = 0
=>a(m – n) + {m (m – 1) – n(n – 1)} d = 0
=> a(m – n) + (m – n) (m + n – 1) d = 0
=> (m – n) {a + (m + n – 1) d} = 0
=> a + (m + n – 1) d = 0
=> am+n = 0
Hence, the (m + n)th term of the given A.P. is zero.
 
Q.- If the pth term of an A.P. is q and the qth term is p, prove that its nth term is (p + q – n).
 
Sol Let a be the first term and d be the common difference of the given A.P. Then,
pth term = q => a + (p – 1) d = q ....(i)
qth term = p => a + (q – 1) d = p ....(ii)
Subtracting equation (ii) from equation (i),we get
(p – q) d = (q – p) => d = – 1
Putting d = – 1 in equation (i), we get
a = (p + q – 1)
nth term = a + (n – 1) d
= (p + q – 1) + (n – 1) × (–1) = (p + q – n)
 
 
SECTION A: 
 
1. Check whether the sequence formed with an =2n2 forms an A.P.
 
2. Find an A.P., if the nth term of an A.P is 5 – 2n.
 
3. If the sum of first n terms of an A.P. is 2n2 + 5n, then find its nth term.
 
4. If 4/5, a and 2 are three consecutive terms of an A.P., then find the value of a.
 
5. If the sum of first p terms of an A.P. is ap2 + bp, find its common difference.
 
6. Find the next term of an A.P. √8 , √18,√32, …..
 
7. Find the common difference of the A.P. (-9-4a), (-8-3a), (-7-2a),……
 
8. For what value of k, (2k+1), 8, 3k form an A.P.?
 
9. Find the missing terms of the A.P. 23, ____, 69,____.
 
10. Find the nth term of the A.P. -2, -5, -8, …..
 
SECTION B: 
 
11. Which term of the A.P 36, 31, 26, 21, … is the first negative term?
 
12. Is 497 a term of the A.P 56, 63, 70, ….?
 
13. Find the 6th term from the end of the A.P. 17, 14, 11, …. – 40.
 
14. Which term of the A.P 3, 10, 17,…. Will be 84 more than its 13th term?
 
15. Show that (a – b), a, (a + b) are in A.P.
 
16. How many numbers of three digits are divisible by 7?
 
17. Which term of the A.P. 18, 16, 14, …… is zero?
 
18. Find the sum of first n odd natural numbers?
 
19. The sum of n terms of an A.P is n2 + 3n. Find its 20th term.
 
20. Find the sum of first 225 natural numbers.
 
SECTION C: 
 
21. Find the sum of the first 25 terms of an A.P. whose nth term is given by an = 2 – 3n.
 
22. If m times the mth term of an A.P. is equal to n times its nth term, find its (m + n)th term.
 
23. The 4th and 10th terms of an A.P. are 13 and 25 respectively. Find the A.P.
 
24. If the sum of the first 14 terms of an A.P is 1050 and its first term is 10, find the 20th term.
 
25. Find the three terms of an A.P. whose sum is 15 and their product is 105.
 
26. If fifth term of an A.P. is zero, show that its 33rd term is four times its 12th term.
 
27. How many terms of the AP 21, 18, 15, …..must be added to get the sum zero?
 
28. The 8th of an AP is equal to three  times its third term. If 6th term is 22, find the AP.
 
29. Determine the A.P. whose fourth term is 18 and the difference of the 9th term from the 15th term is 30.
 
30. The 9th term of an AP is 499 and 499th term is 9, find the term which is equal to zero.
 
SECTION D: 
 
31. In an AP, the first term is 2, the last term is 29 and the sum of all its terms is 155. Find the common difference of the AP.
 
32. The angles of a quadrilateral are in AP whose common difference is 10°. Find the angles.
 
33. The sum of first q terms of an AP is 63 – 3q2. If its pth term is –60, find the value of p. Also, find the 11th term of the AP.
 
34. The first and the last terms of an AP., are – 4 and 146 respectively and the sum of the AP is 7171. Find the number of terms in AP. And the common difference.
 
35. Find the sum of all two digit numbers, which leave 1 as remainder, when divided by 3.
 
36. How many terms of the AP 24, 21, 18, ….must be taken so that their sum is 78?
 
37. Find the 31st term of an AP whose 11th term is 38 and 16th term is 73.
 
38. Find the sum of first 24 terms of the list of numbers whose nth term is given by an = 3 + 2n.
 
39. If pth ,qth and rth terms of an AP are a , b and c respectively, then show that a(q – r) + b(r – p) + c(p – q) = 0.
 
40. A club consists of members whose ages are in AP., common difference being 3 months. The youngest member of the club is just 7 years old and the sum of the ages of members is 250 years. Find the number of members in the club.

 

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Chapter 05 Arithmetic Progression Practice Sheet and Solutions for Class 10 Mathematics

CBSE Practice Material: Class 10 Mathematics Chapter 05 Arithmetic Progression

Review targeted practice exercises for Class 10 Mathematics Chapter 05 Arithmetic Progression. Curated to match official CBSE guidelines, these downloadable PDF sheets support daily revision and core concept reinforcement.

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FAQs

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Are these Mathematics Class 10 worksheets based on the 2026-27 competency-based pattern?

Yes, our CBSE Class 10 Mathematics Arithmetic Progressions Worksheet Set 01 includes a variety of questions like Case-based studies, Assertion-Reasoning, and MCQs as per the 50% competency-based weightage in the latest curriculum for Class 10.

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