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Mathematics - Sequences and Series

Practise 182 NDA previous year questions on Sequences and Series, compiled from papers spanning 2010 to 2026. Each question is pulled directly from the actual exam paper it appeared in, so you're practising in the exact style and difficulty NDA tests.

Sequences and Series has been asked in 17 of the 21 years of NDA papers analysed (2006–2026), with 182 questions in all. 18% of them were easy, 80% moderate and 2% tough. Most of its questions came from 2023, with 15 questions that year. In the last three years (2024–2026) it had 28 questions across 5 papers, about 5.6 per paper.

The chapter's 8 topics are not weighted equally: Arithmetic Progression (88 questions, 48%), Geometric Progression (53 questions, 29%), and Means (16 questions, 9%) have been asked the most. Arithmetic Progression has also led over the last five years, with 34 questions. Arithmetic Progression has produced the most tough questions (3).

  1. 1Let , and be three unequal numbers such that , and are in AP. If , and are in GP, then equals2026 (Phase 1)Arithmetic Progression
  2. 2If , , and are in GP and is the arithmetic mean of and , then is equal to2026 (Phase 1)Geometric Progression
  3. 3The sum of the first terms of an AP is . If the term of the AP is , then what is the value of ?2026 (Phase 1)Arithmetic Progression
  4. 4If term of an AP is , then what is the sum of term, term and term of the AP ?2026 (Phase 1)Arithmetic Progression
  5. 5Passage: Let , and be the points such that , and are in AP. Question: If , and are not in AP and , then the line joining the points , and is2026 (Phase 1)Arithmetic Progression
  6. 6The sum of the first terms of a series is . Which one of the following is correct?2025 (Phase 1)Arithmetic Progression
  7. 7The sum of the first 8 terms of a GP is five times the sum of its first 4 terms. If is the common ratio, then what is the number of possible2025 (Phase 1)Geometric Progression
  8. 8If 5th, 7th and 13th terms of an AP are in GP, then what is the ratio of its first term to its common difference?2025 (Phase 1)Mixed Question on AP and GP
  9. 9If , , are in AP and , , are in GP, then which of the following statements is/are correct? I. , , are in HP. II. , , are in AP. Select the a2025 (Phase 1)Means
  10. 10If , and are in AP, then consider the following statements: I. The GM of and is . II. The AM of and is . Which of the statements given above2025 (Phase 2)Arithmetic Progression
  11. 11How many terms of the series amount to a sum equal to ?2025 (Phase 2)Arithmetic Progression
  12. 12How many terms are identical in the two APs up to 110 terms and up to 75 terms?2025 (Phase 2)Arithmetic Progression
  13. 13For the following two (02) items: Let , where m n$?2025 (Phase 2)Arithmetic Progression
  14. 14For the following two (02) items: Let , where m$ are possible?2025 (Phase 2)Arithmetic Progression
  15. 15What is the harmonic mean of the numbers , , , and ?2025 (Phase 2)Means
  16. 16If are in are in , are in HP, then which of the following is/are correct? 1. and are in GP 2. are in GP Select the correct answer using the 2024 (Phase 1)Arithmetic Progression
  17. 17If are in HP, then what is equal to? 1. 2. 3. Select the correct answer using the code given below:2024 (Phase 1)Harmonic Progression
  18. 18An edible oil is sold at the rates rupees per litre in four consecutive years. Assuming that an equal amount of money is spent on oil by a f2024 (Phase 1)Means
  19. 19Let . The index is given a positive integral value at random. What is the probability that the value of will have 1 in the units place?2024 (Phase 1)Geometric Progression
  20. 20What is equal to?2024 (Phase 1)Summation of Series
  21. 21If times the term of an AP is equal to times the term , then what is the term equal to?2024 (Phase 2)Arithmetic Progression
  22. 22Let and , where . Which of the following statements is/are correct? A. and are in AP. B. and can never be in GP. Select the answer using the2024 (Phase 2)Arithmetic Progression
  23. 23Let be in GP. Then are2024 (Phase 2)Geometric Progression
  24. 24If the sum of the first terms of a series is , then what is the th term?2024 (Phase 2)Arithmetic Progression
  25. 25In an , the ratio of the sum of the first terms to the sum of the first terms is . Which one of the following is correct?2024 (Phase 2)Arithmetic Progression
  26. 26Paragraph: The product of 5 consecutive terms of an AP is 229635. The first, second and fifth terms are in GP. Question: What is the common 2024 (Phase 2)Arithmetic Progression
  27. 27Paragraph: The product of 5 consecutive terms of an AP is 229635 . The first, second and fifth terms are in GP. Question: What is the sum of2024 (Phase 2)Arithmetic Progression
  28. 28The mean of observations is 130 . What is the value of ?2024 (Phase 2)Arithmetic Progression
  29. 29If are in GP, then which one of the following is correct?2023 (Phase 1)Geometric Progression
  30. 30The first and the second terms of an AP are and respectively. If terms is the largest negative term, what is the value of ?2023 (Phase 1)Arithmetic Progression
  31. 31In an AP, the first term is and the sum of the first terms is zero. What is the sum of next terms?2023 (Phase 1)Arithmetic Progression
  32. 32and s are in AP such that and . What is the difference between largest and smallest numbers?2023 (Phase 1)Arithmetic Progression
  33. 33Paragraph: Consider the sum Question: If the sum is divided by 60 , what is the remainder?2023 (Phase 1)Summation of Series
  34. 34Paragraph: Given that , where is a fixed positive real number. Question: What is the least value of ?2023 (Phase 1)Inequalities
  35. 35If G is the geometric mean of numbers , then what is the value of ?2023 (Phase 1)Geometric Progression
  36. 36If is the harmonic mean of numbers , , then what is equal to?2023 (Phase 1)Harmonic Progression
  37. 37If the term of a sequence is , then what is the sum of its first 140 terms?2023 (Phase 2)Arithmetic Progression
  38. 38If are in HP, then which one of the following is correct?2023 (Phase 2)Harmonic Progression
  39. 39Let be in GP. What is equal to?2023 (Phase 2)Geometric Progression
  40. 40Let be in AP such that What is equal to?2023 (Phase 2)Arithmetic Progression
  41. 41Let be in AP such that What is equal to?2023 (Phase 2)Arithmetic Progression
  42. 42What is the mean of the numbers with frequencies , respectively?2023 (Phase 2)Means
  43. 43If H is the Harmonic Mean of three numbers , and , then what is the value of ?2023 (Phase 2)Harmonic Progression
  44. 44What is the value of2022 (Phase 1)Summation of Series
  45. 45If are in GP where , then which of the following are correct? 1. are in GP 2. are in GP 3. are in GP Select the correct answer using the cod2022 (Phase 1)Geometric Progression
  46. 46If are in HP, then which one of the following is correct?2022 (Phase 1)Harmonic Progression
  47. 47If the sum of the first 9 terms of an AP is equal to sum of the first 11 terms, then what is the sum of the first 20 terms?2022 (Phase 1)Arithmetic Progression
  48. 48If the 5th term of an AP is and its 10 th term is , then what is the sum of first 50 terms?2022 (Phase 1)Arithmetic Progression
  49. 49What is the arithmetic mean of 50 terms of an AP with first term 4 and common difference 4 ?2022 (Phase 1)Arithmetic Progression
  50. 50The marks obtained by 51 students in a class are in AP with its first term 4 and common difference 3 . What is the mean of the marks?2022 (Phase 1)Arithmetic Progression

Frequently Asked Questions

1.How many questions are available for Sequences and Series?

This chapter includes 182 questions compiled from NDA papers spanning 2010 to 2026.

2.Are these questions only from NDA, or from other exams too?

These are NDA questions specifically for the Sequences and Series chapter. Questions from other exams like JEE Main or NTA Abhyas (JEE Main) are organised separately under their respective exam sections.

3.Is Sequences and Series an important chapter for NDA Mathematics?

Sequences and Series has appeared in 17 of the 17 years of NDA papers covered here, with 182 questions across 32 papers - about 6 per paper it appears in.

4.What is the difficulty level of Sequences and Series questions in NDA?

Of the 182 questions analysed for this chapter, 18% are easy, 80% moderate and 2% tough. 2023 had the most, with 15 questions.

5.Which topics in Sequences and Series should I focus on?

These topics have carried the most weightage in Sequences and Series:

  • Arithmetic Progression - 88 questions (48%)
  • Geometric Progression - 53 questions (29%)
  • Means - 16 questions (9%)
  • Arithmetic Progression has produced the most tough questions (3).
6.Is Sequences and Series's weightage in NDA going up or down?

Across all 32 papers analysed, Sequences and Series has averaged about 5.7 questions per paper. In the last three years (2024–2026), that average has stayed about the same, at about 5.6 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.