Arithmetic Progression Questions 

In  Arithmetic Progression Questions are essential for scoring well in the CBSE board exams 2022-2023. This chapter deals with sequences that follow a constant pattern or difference between consecutive terms. Whether you're identifying the nth term or calculating the sum of terms, these Arithmetic Progression Questions help you develop clarity and boost confidence.

The following practice set is prepared in alignment with the CBSE syllabus and the latest NCERT patterns, derived after deep research into previous years’ exam trends, board patterns, and sample papers. Students are strongly encouraged to practice these Arithmetic Progression Questions thoroughly to improve their problem-solving speed and accuracy.

Let’s dive into a variety of Arithmetic Progression Questions with detailed solutions and key techniques to crack them.

 

Table of Contents

• What is Arithmetic Progression (AP)?
• Arithmetic Progression Formulas
• Arithmetic Progression Questions with Solutions
• Arithmetic Progression Problems
• Tips for Solving Arithmetic Progression Questions
• Common Mistakes to Avoid
• Real-Life Applications of AP
• Conclusion
• FAQs on Arithmetic Progression Questions

 

What is Arithmetic Progression (AP)?

An Arithmetic Progression (AP) is a number sequence where each term differs from the previous one by a constant value called the common difference. For example, the sequence 2, 5, 8, 11… has a common difference of 3.

In CBSE Class 10, Arithmetic Progression Questions often revolve around:

• Identifying the nth term

• Finding the sum of n terms

• Finding specific terms based on conditions

• Applying AP formulas to solve real-world problems
  
  

Arithmetic Progression Formulas

To master Arithmetic Progression Questions, here are the key formulas:

• nth term (an) = a + (n – 1) × d

• Sum of n terms (Sn) = n/2 × [2a + (n – 1) × d]

• Last term (l) = a + (n – 1) × d
  
  

Where:

• a = First term

• d = Common difference

• n = Number of terms
  
  

These formulas are used repeatedly in board-level Arithmetic Progression Questions.

Arithmetic Progression Questions with Solutions

Q1. Write the first four terms of AP for given a and d:
(i) a = 10, d = 10 → 10, 20, 30, 40
(ii) a = -2, d = 0 → -2, -2, -2, -2
(iii) a = 4, d = -3 → 4, 1, -2, -5

Q2. Which term of AP: 21, 18, 15, … is –81? Is any term zero?
A: 35th term is –81. 8th term is 0.

Q3. Check if –150 is a term of AP: 11, 8, 5, 2
A: No, n is fractional, so –150 is not a term.

Q4. If 3rd term = 4, and 9th = –8, find the term that is 0
A: 5th term is 0.

Q5. Which term is 132 more than the 54th term in AP: 3, 15, 27,…?
A: 65th term.

Q6. How many multiples of 4 between 10 and 250?
A: 60 terms.

Q7. If a₄ + a₈ = 24 and a₆ + a₁₀ = 44, find the first 3 terms.
A: –13, –8, –3.

Q8. Ramkali saves Rs.5 in week 1, increasing by Rs.1.75 weekly. In which week does she save Rs.20.75?
A: 10th week.

Q9. How many terms of AP 24, 21, 18,… make the sum 78?
A: 4 or 13 terms.

Q10. First term = 5, Last term = 45, Sum = 400. Find n and d.
A: n = 16, d = 8/3

Q11. d = 7, 22nd term = 149. Find the sum of first 22 terms.
A: 1661

Q12. Sn = 4n – n². Find a₁, a₂, a₃, a₁₀, aₙ
A: a₁ = 3, a₂ = 1, a₃ = –1, a₁₀ = –15, aₙ = 5 – 2n

Q13. Rs.700 distributed in 7 AP cash prizes, each Rs.20 less. Find the value of prizes.
A: Rs.160, 140, 120, 100, 80, 60, 40

Q14. a₃ + a₇ = 6 and a₃ × a₇ = 8. Find sum of first 16 terms.
A: S₁₆ = 76 or 20 depending on d.

Q15. Houses 1 to 49. Show that there’s an x such that sum before x = sum after x.
A: x = 35

 

Arithmetic Progression Problems

1. Show that (a – b)², a² + b², (a + b)² are in AP.

2. Find common difference: (1/a), (3 – a)/3a, (3 – 2a)/3a

3. Which term of AP –7, –12, –17,… is –82? Is –100 a term?

4. How many terms of AP 45, 39, 33,… make sum = 180?

5. If d = –4, and a₇ = 4, find first term a.

6. Four consecutive AP terms sum to 32, and product ratio is 7:15. Find terms.

7. If a₂₁ – a₇ = 84, find common difference.

8. Which term of 20, 19¼, 18½,… is the first negative term?

9. If ratio of sums of two APs is (7n + 1):(4n + 27), find ratio of 9th terms.

10. 4th term = 0. Prove 25th = 3 × 11th term.
    
    

All these questions are curated based on important Arithmetic Progression Questions that frequently appear in Class 10 board exams.

 

Tips for Solving Arithmetic Progression Questions

• Always identify a and d first.

• Apply nth term or sum formulas accurately.

• If an unknown term is mentioned, treat it as the nth term.

• Convert real-life problems into AP format before solving.

• Solve step-by-step and double-check each formula substitution.
  
  

Common Mistakes to Avoid

• Mixing up n and a in formulas

• Forgetting to subtract 1 when using (n – 1) × d

• Assuming all sequences are AP without checking the common difference

• Incorrect simplification in fractional APs
  
  

Real-Life Applications of AP

• Salary increments over time

• Saving patterns (weekly or monthly)

• Distributing prizes or rewards

• Construction and design spacing

• Scheduling evenly spaced tasks
  
  

Understanding these real-life scenarios helps relate better to Arithmetic Progression Questions in exams.

Conclusion

Practicing Arithmetic Progression Questions boosts your speed, accuracy, and conceptual clarity for board exams. By mastering formulas and solving pattern-based questions, you can score full marks in this section of the paper. Don’t just read -practice these solved examples and attempt more questions to feel confident and exam-ready.

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Frequently Asked Questions on Arithmetic Progression Questions

1. Are these Arithmetic Progression Questions from NCERT Class 10?

 Yes, all questions align with the NCERT Class 10 CBSE Maths Chapter 5 syllabus.

2. How many marks are AP questions typically worth in board exams?

They often account for 3–6 marks depending on question types.

3. Which formula is most important in AP?

The nth term and sum of n terms formulas are the most used.

4. Can AP questions come in case-study format?

 Yes, recent exams have included AP-based case-study problems.

5. What’s the best way to prepare for Arithmetic Progression Questions?

 Practice daily with questions from NCERT, sample papers, and previous year exams.

 

Master every type of Arithmetic Progression Question for Class 10 - scroll up, practice now, and score top marks in your CBSE board exam. Learn more with Orchids International !