NCERT solutions for Class 11 Mathematics Chapter 8 Sequences and Series – complete answers & explanations

Class 11 Mathematics Chapter 8 Sequences and Series introduces students to the fundamental concepts of sequences, series, arithmetic progressions, and geometric progressions. This chapter builds a strong foundation for higher-level mathematics by helping students understand patterns, relationships between numbers, and formulas used to find terms and sums. It plays an important role in improving logical reasoning and problem-solving skills, which are essential for exams and competitive tests. Students often find this chapter challenging, so having clear and reliable NCERT solutions can make learning much easier. This blog provides step-by-step answers aligned with NCERT answers to help students practice effectively and build confidence. Download the worksheet and practice alongside solutions for better clarity. Book a free trial now to get expert guidance.

What this NCERT chapter covers?

1. Understanding sequences as ordered lists of numbers and how patterns are formed.
2. Learning how to find the nth term of a sequence using given formulas.
3. Introduction to arithmetic progression (A.P.) and geometric progression (G.P.).
4. Methods to calculate specific terms like a₂, a₇, a₁₇, etc.
5. Understanding series as the sum of sequence terms.
6. Learning how to write series from given sequences.
7. Concepts of geometric series and their applications.
8. Formulas to calculate the sum of n terms in different progressions.
9. Solving real-life problems using sequences and series concepts.
10. Developing analytical thinking and step-by-step problem-solving skills.

How to use these NCERT solutions?

1. First, attempt all questions from the worksheet on your own without looking at the answers.
2. Carefully compare your answers with the given solutions to identify mistakes.
3. Focus on understanding the pattern or logic behind each sequence or series.
4. Rework incorrect answers to strengthen your concepts.
5. Use these solutions to revise before exams and improve speed and accuracy.
6. Follow the exact order of questions to stay aligned with the worksheet structure.
7. Parents and teachers can guide students by discussing mistakes and clarifying doubts.
8. Practice regularly to build confidence in solving sequence-based problems.

Important tips & tricks for students

1. Always identify the pattern in a sequence before attempting to write terms.
2. Pay attention to signs (positive/negative) in sequences and series.
3. Memorize key formulas for arithmetic and geometric progressions.
4. Avoid skipping steps while solving problems, especially in exams.
5. Double-check calculations to prevent simple arithmetic errors.
6. Practice writing series clearly to avoid confusion.
7. Understand the difference between sequence and series carefully.
8. Revise formulas regularly to improve speed and accuracy.
9. Focus on concept clarity rather than rote learning.
10. Attempt a variety of problems to strengthen understanding.

NCERT solutions – complete answer key

EXERCISE 8.1

Write the first five terms of each of the sequences in Exercises whose nth terms are:

1 Answer: 3, 8, 15, 24, 35 
2 Answer: 1/2, 2/3, 3/4, 4/5, 5/6 
3 2, 4, 8, 16, 32 
4 -1/6, -1/3, -1/2, -2/3, -5/6 
5 6, -11, 16, -21, 26 
6 6, 9/2, 14/3, 21/4, 30/5 

Find the indicated terms in each of the sequences in Exercises 7 to 10 whose nth terms are:

7 a17 = 65, a24 = 93 
8 a2 = 1/2, a7 = 1/128 
9 a9 = 729 
10 a20 = -40 

Write the first five terms of each of the sequences in Exercises 11 to 13 and obtain the corresponding series:

11 3, 11, 35, 107, 323 
Series: 3 + 11 + 35 + 107 + 323 + ... 

12 -1, -1/2, -1/6, -1/24, -1/120 

13 2, 2, 1, 1, 0 
Series: 2 + 2 + 1 + 1 + 0 + ... 

14 1, 2, 3/2, 5/3, 8/5 

EXERCISE 8.2

1 a20 = 5 × (1/2)^19 
an = 5 × (1/2)^(n-1) 

2 12th term = 3072 

3 q² = ps 

4 a7 = -192 

5 (a) 8th term = 128 
(b) 7th term = 729 
(c) ? = 8th term → 19683 corresponds to 9th term 

6 x = ±7 

Find the sum to indicated number of terms in each of the geometric progressions in Exercises 7 to 10:

 

7 Sum = 0.166666… 

8 Sn = (7(3^n - 1))/2 

9 Sn = (1 - (-a)^n)/(1 + a) 

10 Sn = x^3(1 - x^(2n))/(1 - x^2) 

11 6141 

12 r = -3/4 or -4/3 
Terms: (4/3, -1, 3/4) or (3/4, -1, 4/3) 

13 n = 6 

14 a = 2, r = 2 
Sn = 2(2^n - 1) 

15 S7 = 1093 

16 a = -2, r = 2 

17 x, y, z are in G.P. 

18 Sn = (8/9)[(10^n - 1) - n] 

19 Sum = 272 

20 Common ratio = r × R 

21 Numbers: 2, 4, 8, 16 

22 a^(q−r) · b^(r−p) · c^(p−q) = 1 

23 P² = (ab)^n 

24 Ratio = 1/r^n 

25 (a² + b² + c²)(b² + c² + d²) = (ab + bc + cd)² 

26 9, 27 

27 n = 1/2 

28 Ratio = (3 + 2√2) : (3 − 2√2) 

29 Numbers = A ± √(A² − G²) 

30 2nd hour = 120 
4th hour = 480 
nth hour = 30 × 2^n 

31 1296.87 

32 x² − 16x + 25 = 0 

MISCELLANEOUS EXERCISE

1 n = 4 

2 Last term = 160, n = 6 

3 r = ±3 

4 Numbers: 8, 16, 32 

5 r = 1/2 

6 The given relation holds true, hence proved. 

7 P²R^n = S_n 

8 (b^n + c^n)/(a^n + b^n) = (c^n + d^n)/(b^n + c^n) = r^n → Hence proved. 

9 (q + p) : (q − p) = 17 : 15 

10 The required identity is verified, hence proved. 

11 (i) Sn = (5/9)[(10^n − 1) − n] 
(ii) Sn = (2/3)[(10^n − 1) − n] 

12 20th term = 760 

13 Total cost = 15600 

14 Total cost = 26000 

15 Amount = 655.36 

16 15th year = 17500 
20 years total = 20000 

17 Value = 5120 

18 Days = 20 

Why NCERT solutions help students?

NCERT solutions help students build strong conceptual clarity, improve accuracy in problem-solving, and prepare effectively for exams. By practicing well-structured answers, students gain confidence and learn the correct approach to solving mathematical problems, which is essential for scoring high marks.

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