NCERT Solutions for Class 11 Maths Chapter 8 Sequences and Series
NCERT Solutions for Class 11 Maths Chapter 8 Sequences and Series
NCERT Solutions for Class 11 Maths Chapter 8 Sequences and Series
This worksheet for Class 11 Mathematics Chapter 8 Sequences and Series helps students understand the concepts of sequences, series, and their applications in a clear and structured way. This worksheet provides complete and accurate NCERT Solutions that strictly follow the NCERT pattern and question format. The chapter is important because it builds a strong foundation in algebra and helps students develop problem-solving skills required for higher mathematics.
Chapter summary: stories, poems & themes
This chapter is concept-based and focuses entirely on mathematical patterns, sequences, and series. There are no stories or poems in this worksheet. Students learn how numbers follow patterns, how sequences are formed, and how to calculate terms and sums. The main theme of the chapter is understanding numerical patterns and applying formulas to find required terms and sums. The worksheet is fully exercise-based and focuses on problem-solving.
What this NCERT chapter covers?
• Understanding sequences and their nth term
• Writing terms of sequences using given formulas
• Finding specific terms in sequences
• Understanding series and writing them from sequences
• Learning arithmetic and geometric progressions
• Calculating sums of geometric progressions
• Applying formulas in different problem types
How to use these NCERT solutions?
Students should first attempt each question from the worksheet on their own and then refer to the NCERT Solutions to check their answers. Parents and teachers can use these solutions to guide students and explain step-by-step methods. The solutions follow the exact NCERT order and structure, making it easier for students to revise and understand concepts clearly. Regular practice using this worksheet improves accuracy and confidence.
Student tips & learning tricks
• Carefully identify the pattern in sequences before solving
• Pay attention to signs (positive and negative terms)
• Practice writing the first few terms to understand the sequence
• Use formulas correctly for geometric progressions
• Avoid calculation mistakes while dealing with powers and fractions
• Double-check answers while finding specific terms
Why NCERT solutions are important?
NCERT Solutions help students learn the correct method of solving problems as per CBSE guidelines. They strengthen conceptual understanding and ensure clarity in each step. These solutions also help students prepare effectively for exams by improving accuracy and speed. Strong practice with NCERT Solutions builds confidence and supports long-term learning.
Complete answer key – NCERT solutions
Exercise 8.1
1. 3, 8, 15, 24, 35
2. 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
7. a17 = 65, a24 = 93
8. a2 = 1/2, a7 = 1/128
9. a9 = 729
10. a20 = -40
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
12th term = 3072
6. x = ±7
Find the sum to indicated number of terms in geometric progressions
7. Sum = 0.166666…
8. Sn = (7(3^n - 1))/2
9. Sn = (1 - (-a)^n)/(1 + a)
10. Sn = x³(1 - x^(2n))/(1 - x²)
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. P² R^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
Master Class 11 Maths Chapter 8 Sequences and Series with accurate NCERT Solutions and improve your problem-solving skills with expert-guided practice.