CBSE Class 10 Mathematics • Chapter 5
Arithmetic Progression Class 10 Worksheet with Solutions
Practise common difference, the nth term and the sum of an arithmetic progression. Revise the formulas, follow worked examples and test your understanding with MCQs, reasoning questions and a seating-plan case study.
This Arithmetic Progression Class 10 worksheet helps you recognise number patterns and use them to solve problems efficiently. Instead of writing every term in a long sequence, you can calculate a particular term or a total using the first term, common difference and number of terms.
Use the worksheet available on this page alongside the explanations and original practice questions below. This worksheet on Arithmetic Progression Class 10 supports homework, classroom practice and revision. Show your calculations clearly, then check whether your answer represents a term, its position or the sum of several terms.
What Is Arithmetic Progression?
An arithmetic progression, usually written as AP, is a sequence in which the difference between consecutive terms is constant. This fixed difference is called the common difference and is denoted by d.
Arithmetic Progression Example
4, 9, 14, 19, 24, …
First term: a = 4
Common difference: d = 9 − 4 = 5
The differences 14 − 9, 19 − 14 and 24 − 19 also equal 5. Therefore, the sequence is an AP.
General form: a, a + d, a + 2d, a + 3d, …
| Sequence | Common Difference | Is It an AP? |
|---|---|---|
| 3, 7, 11, 15, … | 4 | Yes |
| 20, 16, 12, 8, … | −4 | Yes |
| 6, 6, 6, 6, … | 0 | Yes |
| 1/2, 1, 3/2, 2, … | 1/2 | Yes |
| 2, 4, 8, 16, … | Differences are 2, 4 and 8 | No |
Class 10 Arithmetic Progression Formulas
Let a be the first term, d the common difference, n the number of terms, an the nth term and Sn the sum of the first n terms. In a finite AP, l denotes the last term.
| Concept | Formula |
|---|---|
| Common difference | d = a2 − a1 |
| nth term | an = a + (n − 1)d |
| Sum of the first n terms | Sn = n[2a + (n − 1)d] / 2 |
| Sum when the first and last terms are known | Sn = n(a + l) / 2 |
| Difference between two terms | am − an = (m − n)d |
| nth term from sums, for n ≥ 2 | an = Sn − Sn−1 |
| kth term from the end of a finite AP | l − (k − 1)d |
Choose the Formula That Matches the Question
Use an for a particular term and Sn for a total. If a question asks “Which term is 79?”, solve for n. A term position must be a positive integer.
Class 10 Arithmetic Progression Questions with Solutions
Example 1: Find the 20th Term
Question: Find the 20th term of 7, 11, 15, 19, …
a = 7
d = 4
n = 20
an = a + (n − 1)d
a20 = 7 + (20 − 1) × 4
a20 = 7 + 76
a20 = 83
Example 2: Find the Position of a Term
Question: Which term of 4, 9, 14, 19, … is 79?
a = 4
d = 5
an = 79
79 = 4 + (n − 1) × 5
75 = 5(n − 1)
15 = n − 1
n = 16
Answer: 79 is the 16th term.
Example 3: Find the Sum of the First 15 Terms
Question: Find the sum of the first 15 terms of 6, 10, 14, 18, …
a = 6
d = 4
n = 15
Sn = n[2a + (n − 1)d] / 2
S15 = 15[12 + 14 × 4] / 2
S15 = 15 × 68 / 2
S15 = 510
Check using the last term:
a15 = 6 + 14 × 4
a15 = 62
S15 = 15(6 + 62) / 2
S15 = 510
Example 4: Find the AP from Two Given Terms
Question: The 5th term of an AP is 18 and its 12th term is 46. Find the first term and common difference.
a + 4d = 18 … (1)
a + 11d = 46 … (2)
Subtract equation (1) from equation (2):
7d = 28
d = 4
Substitute d = 4 into equation (1):
a + 16 = 18
a = 2
Answer: a = 2 and d = 4. The AP begins 2, 6, 10, 14, 18, …
Arithmetic Progression Class 10 Case Study with Answers
Case Study: Seating in a School Auditorium
A school auditorium has 18 seats in the first row. Each following row has 3 more seats than the previous row. There are 12 rows.
1. Write the AP representing the seats.
18, 21, 24, 27, …
a = 18 and d = 3.
2. How many seats are in the 8th row?
a8 = 18 + (8 − 1) × 3
a8 = 18 + 21
a8 = 39 seats
3. How many seats are in the last row?
a12 = 18 + 11 × 3
a12 = 51 seats
4. Find the total seating capacity.
S12 = 12(18 + 51) / 2
S12 = 6 × 69
S12 = 414 seats
This example shows the difference between a term and a sum: 51 is the number of seats in one row, while 414 is the total number of seats across all rows.
Arithmetic Progression Class 10 HOTS and Reasoning Questions
Can 100 Be a Term of 3, 8, 13, 18, …?
Set the nth term equal to 100:
100 = 3 + (n − 1) × 5
97 = 5(n − 1)
n − 1 = 97/5
n = 102/5
Since n is not an integer, 100 is not a term of this AP. Do not round a term position to make it fit the sequence.
Find the nth Term When the Sum Is Given
Question: If Sn = 2n2 + 3n, find the nth term.
For n ≥ 2:
an = Sn − Sn−1
an =
2n2 + 3n − [2(n − 1)2 + 3(n − 1)]
an =
2n2 + 3n − [2n2 − n − 1]
an = 4n + 1
Also, a1 = S1 = 5, which agrees with the formula. The sequence is 5, 9, 13, 17, … with common difference 4.
Arithmetic Progression Class 10 MCQ with Answers
MCQ 1: Common Difference
What is the common difference of 15, 11, 7, 3, …?
A. 4 B. −4 C. 11 D. −11
Show Answer
Answer: B. −4. Subtract the earlier term from the next term: 11 − 15 = −4.
MCQ 2: nth Term
What is the 10th term of 2, 5, 8, 11, …?
A. 27 B. 29 C. 30 D. 32
Show Answer
Answer: B. 29.
a10 = 2 + 9 × 3 = 29.
MCQ 3: Sum of Terms
What is the sum of the first 10 positive odd integers?
A. 50 B. 90 C. 100 D. 110
Show Answer
Answer: C. 100. The integers are 1, 3, 5, …, 19. Their sum is 10(1 + 19)/2 = 100.
MCQ 4: Constant Sequence
Which statement about 7, 7, 7, 7, … is correct?
A. It is not an AP.
B. It is an AP with d = 7.
C. It is an AP with d = 0.
D. Its common difference changes.
Show Answer
Answer: C. Every consecutive difference is zero. Therefore, it is an AP with d = 0.
Extra Arithmetic Progression Class 10 Practice Questions
Use these original questions as a short test. Write the given values, select the formula and show your substitution before calculating.
- Find the 25th term of 5, 8, 11, 14, …
- Which term of 12, 17, 22, 27, … is 97?
- Find the sum of the first 20 terms of 3, 7, 11, 15, …
- The 4th term of an AP is 14 and its 9th term is 34. Find a and d.
- Find the 5th term from the end of 2, 5, 8, …, 50.
- A student saves ₹50 in the first week and increases the weekly saving by ₹10 each week. Find the total saved in 8 weeks.
Check the Practice Answers
- a25 = 77.
- 97 is the 18th term.
- S20 = 820.
- a = 2 and d = 4.
- 50 − 4 × 3 = 38.
- S8 = ₹680.
Using This Worksheet with NCERT Exercises and Previous Year Questions
For Class 10 Arithmetic Progression Exercise 5.1, practise recognising an AP and identifying its first term and common difference. Build confidence with nth-term questions for Exercise 5.2, then practise sums and applications for Exercise 5.3. Follow the questions and numbering in your own NCERT textbook edition.
Use this practice alongside Arithmetic Progression Class 10 NCERT solutions, sample papers and verified previous year questions. When choosing an Arithmetic Progression Class 10 previous year questions PDF, check the board and examination year. The additional questions on this page are original practice questions.
If you use an Arithmetic Progression Class 10 test paper PDF, complete it without referring to the formula sheet first. Review errors afterwards and reattempt questions involving the same concept. This helps you identify whether you need more practice with term positions, sums or equation formation.
Common AP Mistakes to Avoid
- Using a + nd instead of a + (n − 1)d.
- Ignoring a negative sign in the common difference.
- Using the nth-term formula when the question asks for a total.
- Accepting a fractional value as a term position.
- Confusing the amount saved in the last week with the total saved over all weeks.
- Assuming every increasing sequence is an AP without checking consecutive differences.
Arithmetic Progression Class 10 Notes, Mind Map and Solutions
FAQs on Arithmetic Progression Class 10 Worksheet
What is arithmetic progression? Give an example.
An arithmetic progression is a sequence with a constant difference between consecutive terms. For example, 4, 9, 14, 19, … is an AP because each term is 5 more than the preceding term.
How do I check whether a sequence is an AP?
Subtract each term from the next term. If all consecutive differences are equal, the sequence is an AP. For example, 2, 6, 10, 14 has differences 4, 4 and 4. The sequence 2, 4, 8, 16 has changing differences and is not an AP.
Can the common difference be negative or zero?
Yes. In 12, 9, 6, 3, …, the common difference is −3. In 5, 5, 5, 5, …, it is 0. An AP can increase, decrease or remain constant.
What is the nth-term formula for Class 10 arithmetic progression?
The formula is an = a + (n − 1)d. For example, in 3, 7, 11, …, a = 3 and d = 4. The 10th term is 3 + 9 × 4 = 39.
Why does the nth-term formula use n − 1?
There are n − 1 steps from the first term to the nth term. The second term adds d once, the third adds it twice and the fourth adds it three times. Therefore, the nth term adds d exactly n − 1 times.
What is the difference between an and Sn?
an is one term at position n. Sn is the total of the first n terms. For 2, 4, 6, 8, …, the fourth term is 8, while the sum of the first four terms is 20.
How do I find the sum of the first n terms?
Use Sn = n[2a + (n − 1)d]/2. If the first term a and last term l are known, use Sn = n(a + l)/2. Both formulas give the same total.
How do I check whether a number belongs to an AP?
Set a + (n − 1)d equal to the given number and solve for n. A positive integer value gives its position. If the result is fractional, zero or negative, the number is not a term of that AP. For a finite AP, the position must also lie within its length. If d = 0, every term equals a, so check whether the given number is a.
How can I find a and d when two terms are given?
Express both terms using an = a + (n − 1)d. Subtract the resulting equations to find d, then substitute it back to find a. For example, the 5th and 12th terms differ by 7d.
How do I find the nth term when the sum formula is given?
For n ≥ 2, subtract Sn−1 from Sn. Find the first term separately using a1 = S1. For example, Sn = 2n2 + 3n gives an = 4n + 1.
Which Arithmetic Progression Class 10 HOTS questions should I practise?
Practise term-membership questions, finding an AP from two terms, recovering terms from sums and comparing terms without calculating each one separately. Include word problems that require you to distinguish a single term from a total.
How should I use an Arithmetic Progression Class 10 PDF with solutions?
Attempt the questions before reading the answers. Compare your formula choice, substitution and calculations with the solution. Reattempt incorrect questions without help, especially those involving negative differences or the number of terms.
Where can I find Arithmetic Progression Class 10 notes and a mind map?
Visit the Arithmetic Progressions Class 10 Notes and Mind Map on WitKnowLearn. Use it for concept revision before returning to this worksheet.
Where are Maharashtra Board Maths 1 Chapter 3 solutions?
Use the Class 10 Maths 1 Chapter 3 Arithmetic Progression Solutions . Maharashtra Board and CBSE textbooks use different chapter and exercise numbering, so match the resource to your textbook.
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