Students preparing for their Class 11 Maths board exams will find Chapter 19 – Arithmetic Progressions from the RD Sharma textbook especially important. In this chapter, an Arithmetic Progression (A.P.) is defined as a number sequence where the difference between consecutive terms is always constant. To build a solid foundation in CBSE Class 11 Mathematics, RD Sharma’s book is an ideal reference. This chapter includes seven exercises, and the solutions provided here offer detailed explanations and step-by-step answers for every question to support students’ learning. These solutions are designed by experienced subject teachers who understand the academic level and needs of Class 11 students. For added convenience, PDF links to the solutions are available below, making it easier to access and revise anytime.
RD Sharma Solutions Class 11 Maths Chapter 19 - Overview
- Understanding Sequences
- What is an Arithmetic Progression (A.P.)
- How to Find the General Term of an A.P.
- Choosing Specific Terms from an A.P.
- Formula to Find the Sum of First ‘n’ Terms
- Key Properties of Arithmetic Progressions
- How to Insert Arithmetic Means Between Numbers
- Practical Uses and Applications of A.P.
These solutions are a great tool for daily practice and concept revision, helping students score better in exams with clear understanding.
RD Sharma Solutions Class 11 Maths Arithmetic Progressions Question with Solutions
35 Important Questions with Solutions
Basic Concepts and General Term
Q1. Write the first five terms of the A.P. whose first term is 2 and common difference is 4.
Solution: a = 2, d = 4 → 2, 6, 10, 14, 18
Q2. Find the 10th term of the A.P.: 5, 9, 13,...
Solution: a = 5, d = 4 → T₁₀ = 5 + 9×4 = 41
Q3. Which term of the A.P. 3, 8, 13, 18,... is 98?
Solution: Tn = a + (n – 1)d → 98 = 3 + (n – 1)×5 → n = 20
Q4. Is 145 a term of the A.P. 4, 9, 14,...?
Solution: Tn = 4 + (n – 1)×5 = 145 → n – 1 = 28.2 → Not an integer → No
Q5. Find the number of terms in the A.P. 7, 13, 19,..., 139
Solution: Tn = 7 + (n – 1)×6 = 139 → n = 23
Sum of Terms in an A.P.
Q6. Find the sum of the first 20 terms of the A.P. 2, 5, 8,...
Solution: a = 2, d = 3 → Sₙ = 10(4 + 57) = 610
Q7. If the sum of first n terms is 3n² + 2n, find the 10th term.
Solution: T₁₀ = S₁₀ – S₉ = 320 – 261 = 59
Q8. How many terms of the A.P. 12, 11, 10,... add up to 78?
Solution: a = 12, d = –1 → n = 13
Insert Arithmetic Means
Q9. Insert 3 A.M.s between 2 and 14.
Solution: d = (14 – 2)/4 = 3 → Means: 5, 8, 11
Q10. Insert 4 A.M.s between 10 and 30.
Solution: d = (30 – 10)/5 = 4 → Means: 14, 18, 22, 26
Application-Based & Word Problems
Q11. ₹2000 is shared among 25 people in increasing order with ₹5 difference. What is the first term?
Solution: Let a = first amount. S = 25/2 [2a + 24×5] = 2000 → a = ₹20
Q12. If T₅ = 20 and T₁₅ = 60, find a and d.
Solution: 10d = 40 → d = 4 → a = 4
Q13. If T₃ = 9 and T₇ = 25, find T₂₀.
Solution: d = 4, a = 1 → T₂₀ = 77
Q14. Find the sum of all two-digit numbers divisible by 5.
Solution: a = 10, l = 95, d = 5 → n = 18 → S = 945
Q15. If T₈ = 31 and T₁₃ = 49, find a and d.
Solution: d = 3.6, a = 5.8