FSc Part 1 Maths chapter 6: Sequences and series MCQs with answers

By Team Megalecture · Updated 4 Nov 2026

28 exam-style questions on Sequences and series, each with the answer and a short explanation. Ten of them are below to try. The chapter test draws ten fresh questions each time and is marked the moment you finish, with your score by topic.

28 questions · 3 topics · 10 per test

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What chapter 6 covers

Ten Sequences and series questions with answers

Try each one, then open the answer. These ten stay the same; the test draws new ones every time.

1. The three arithmetic means between 2 and 18 are

  1. A
    4, 8, 12
  2. B
    6, 11, 16
  3. C
    6, 10, 14
  4. D
    5, 9, 13
Show answer

Answer: C. With 3 means there are 5 terms, so 18 = 2 + 4d and d = 4. The means are 6, 10, 14.

2. The nth term of the H.P. 1/2, 1/5, 1/8, ... is

  1. A
    1/(3n + 2)
  2. B
    1/(3n − 1)
  3. C
    3n − 1
  4. D
    1/(2n + 3)
Show answer

Answer: B. The reciprocals 2, 5, 8, ... have nth term 2 + (n − 1)3 = 3n − 1, so the H.P. has nth term 1/(3n − 1).

3. The sum of the first n natural numbers is

  1. A
    n2
  2. B
    n(n − 1)/2
  3. C
    n(n + 1)/2
  4. D
    n(n + 1)
Show answer

Answer: C. Sn = n/2 (first + last) = n/2 (1 + n). n2 is the sum of the first n odd numbers.

4. Which term of the G.P. 1/2, 1, 2, ... is 64?

  1. A
    7th
  2. B
    8th
  3. C
    9th
  4. D
    6th
Show answer

Answer: B. (1/2)2n−1 = 64 gives 2n−2 = 26, so n − 2 = 6 and n = 8.

5. An infinite G.P. has first term 6 and sum to infinity 9. Its common ratio is

  1. A
    2/3
  2. B
    1/3
  3. C
    3/2
  4. D
    −1/3
Show answer

Answer: B. 6/(1 − r) = 9 gives 1 − r = 2/3, so r = 1/3.

6. The sum of the first 20 terms of 2 + 5 + 8 + ... is

  1. A
    640
  2. B
    580
  3. C
    1220
  4. D
    610
Show answer

Answer: D. Sn = n/2 [2a + (n − 1)d] = 10 [4 + 19 × 3] = 10 × 61 = 610. Forgetting the ½ doubles it.

7. The two harmonic means between 1/3 and 1/12 are

  1. A
    1/4 and 1/8
  2. B
    1/5 and 1/7
  3. C
    1/6 and 1/9
  4. D
    1/6 and 1/10
Show answer

Answer: C. The reciprocals 3, _, _, 12 must be an A.P.: d = 3, giving 6 and 9. So the harmonic means are 1/6 and 1/9.

8. The sum of the first 5 terms of 3 − 6 + 12 − ... is

  1. A
    93
  2. B
    33
  3. C
    −93
  4. D
    −33
Show answer

Answer: B. a = 3, r = −2: S5 = 3(1 − (−2)5)/(1 − (−2)) = 3(33)/3 = 33. Check: 3 − 6 + 12 − 24 + 48 = 33. Using r = 2 gives 93.

9. The 20th term of the A.P. 3, 7, 11, ... is

  1. A
    79
  2. B
    83
  3. C
    76
  4. D
    80
Show answer

Answer: A. an = a + (n − 1)d = 3 + 19 × 4 = 79. Using n instead of n − 1 gives 83.

10. If a, b, c are in harmonic progression, then

  1. A
    b = ac/(a + c)
  2. B
    b = (a + c)/2
  3. C
    b2 = ac
  4. D
    b = 2ac/(a + c)
Show answer

Answer: D. 1/a, 1/b, 1/c are in A.P., so 2/b = 1/a + 1/c = (a + c)/ac, giving b = 2ac/(a + c).

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Ways to practise this chapter

Sequences and series: questions students ask

How many Sequences and series MCQs are there?

28, each with the answer and a short explanation, across 3 topics: Arithmetic progressions, Geometric progressions, Harmonic progressions and means. Every chapter test draws ten of them, so you can take it many times.

Is the FSc Part 1 Maths chapter 6 test free?

Yes. The test, the answers and the explanations are free and need no sign-up. Sign in only if you want your scores kept across devices.

How is the chapter test marked?

The moment you press Finish: your score, the right answer and an explanation for every question, and the ones you got wrong saved in My mistakes to retry.

Can I read the explanations in Urdu?

Yes. In practice mode and on your results you can switch the explanations to Urdu.

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