NCERT Solutions for Class 10 Mathematics Chapter 5
NCERT solutions for Class 10 Mathematics Chapter Arithmetic Progressions – complete answers & explanations
Arithmetic Progressions is an important chapter in Class 10 Mathematics that helps students understand patterns in numbers and sequences. In this chapter, students learn how numbers increase or decrease in a fixed pattern and how to identify such sequences. This concept is widely used in real-life situations like finance, measurement, and data analysis. Clear understanding of this chapter builds a strong base for higher mathematics and helps in scoring well in exams. This blog provides clear and reliable NCERT solutions that match the expected answering style for students. Download the worksheet and practice alongside solutions for better clarity. Parents can also use these solutions to guide their children step by step. Book a free trial now to get expert guidance.
What this NCERT chapter covers?
1. Understanding the concept of sequences
and patterns in numbers.
2. Learning what an arithmetic progression (AP) is and how to identify it.
3. Recognizing the importance of constant difference between terms.
4. Finding the first term and common difference in a sequence.
5. Writing terms of an AP using given values.
6. Identifying whether a given sequence is an AP or not.
7. Solving practical problems based on real-life situations like cost and fare.
8. Understanding how patterns differ when multiplication is involved instead of addition.
9. Working with integers, fractions, and decimals in sequences.
10. Learning step-by-step calculations for finding terms in AP.
11. Strengthening logical thinking and pattern recognition skills.
12. Preparing for exam-based questions with structured answers.
How to use these NCERT solutions?
1. Start by reading each question
carefully from the worksheet before looking at the answer.
2. Try solving the question on your own using the concept of arithmetic progression.
3. Check your answer with the provided solution to understand the correct approach.
4. Pay attention to how the common difference is calculated in each case.
5. Follow the same order of questions as given in the worksheet for better understanding.
6. Use these answers to revise before exams and improve accuracy.
7. Parents and teachers can guide students by explaining each step clearly.
8. Focus on understanding why a sequence is or is not an AP.
9. Practice similar questions to build confidence and speed.
10. Use mistakes as learning opportunities to improve performance.
Important tips & tricks for students
1. Always check if the difference between consecutive terms is constant.
2. Do not confuse multiplication patterns with arithmetic progression.
3. Carefully calculate differences, especially with negative numbers.
4. Practice writing terms step-by-step instead of skipping steps.
5. Remember that AP requires addition or subtraction, not multiplication.
6. Pay attention to decimal and fraction calculations.
7. Write answers neatly and clearly as shown in solutions.
8. Avoid calculation errors by double-checking your work.
9. Practice regularly to improve speed and accuracy.
10. Understand the concept rather than memorizing answers.
NCERT solutions – complete answer key
Exercise No. 5.1
(i) Taxi fare:
Fare = 15, 23, 31, 39, ...
Difference = 8 (constant)
→ Yes, it is an AP
(iii) Cost of digging:
150, 200, 250, ...
Difference = 50
→ Yes, AP
(i) a = 10, d = 10
First four terms:
10
10 + 10 = 20
20 + 10 = 30
30 + 10 = 40
Answer: 10, 20, 30, 40
(ii) Air removal:
Each time multiplied by 3/4
→ Not constant difference
→ Not an AP
(iv) Compound interest:
Amount increases multiplicatively
→ Not constant difference
→ Not an AP
(ii) a = –2, d = 0
First four terms:
–2
–2 + 0 = –2
–2 + 0 = –2
–2 + 0 = –2
Answer: –2, –2, –2, –2
(iii) a = 4, d = –3
First four terms:
4
4 – 3 = 1
1 – 3 = –2
–2 – 3 = –5
Answer: 4, 1, –2, –5
(iv) a = –1, d = 1/2
First four terms:
–1
–1 + 1/2 = –1/2
–1/2 + 1/2 = 0
0 + 1/2 = 1/2
Answer: –1, –1/2, 0, 1/2
(v) a = –1.25, d = –0.25
First four terms:
–1.25
–1.25 – 0.25 = –1.5
–1.5 – 0.25 = –1.75
–1.75 – 0.25 = –2.0
Answer: –1.25, –1.5, –1.75, –2.0
(i) 3, 1, –1, –3
a = first term = 3
d = 1 – 3 = –2
Answer: a = 3, d = –2
(iv) 0.6, 1.7, 2.8, 3.9
a = 0.6
d = 1.7 – 0.6 = 1.1
Answer: a = 0.6, d = 1.1
(i) 2, 4, 8, 16
Differences:
4 – 2 = 2
8 – 4 = 4
16 – 8 = 8
Differences not same → Not an AP
(ii) –5, –1, 3, 7
a = –5
d = –1 – (–5) = 4
Answer: a = –5, d = 4
(iii) 1/3, 5/3, 9/3, 13/3
a = 1/3
d = 5/3 – 1/3 = 4/3
Answer: a = 1/3, d = 4/3
(ii) Given: 5/2, 3, 7/2, 4, ...
a₂ – a₁ = 3 – 5/2 = 1/2
a₃ – a₂ = 7/2 – 3 = 1/2
a₄ – a₃ = 4 – 7/2 = 1/2
Since the difference is same, it is an AP with d = 1/2
Next three terms: 9/2, 5, 11/2
(iii) –1.2, –3.2, –5.2, –7.2
Differences:
–3.2 – (–1.2) = –2
–5.2 – (–3.2) = –2
–7.2 – (–5.2) = –2
Same difference → AP, d = –2
Next terms: –9.2, –11.2, –13.2
Why NCERT solutions help students?
NCERT solutions help students understand the correct method of solving questions and improve their problem-solving skills. They provide clarity of concepts, help in exam preparation, and ensure that answers are written in the expected format. With regular practice, students gain confidence and perform better in Mathematics.
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