Sequences and Progressions Class 9 MCQs (100 Questions with Answers) | Latest 2026 Pattern

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Understanding Sequences and Progressions is essential for building strong mathematical thinking. This chapter introduces patterns, logical reasoning, and real-life applications like growth, finance, and puzzles.

👉 In this post, you will find 100 carefully designed MCQs based on the latest 2026 syllabus, covering all important concepts like AP, GP, recursive rules, and more.

✔ Arithmetic Progression nth term:
aₙ = a + (n−1)d

✔ Geometric Progression nth term:
aₙ = a × rⁿ⁻¹

✔ Sum of first n natural numbers:
Sₙ = n(n+1)/2

💡 Tip: If difference is constant → AP
If ratio is constant → GP

👉 Answers to all 100 MCQs are provided at the end of the post.

100 MCQs – Sequences & Progressions (Class 9)

🔹 Questions 1–10

  1. The next term in sequence 2, 4, 6, 8 is
    A) 9 B) 10 C) 12 D) 14
  2. The sequence 3, 6, 9, 12 is
    A) GP B) AP C) Neither D) Both
  3. Common difference of 5, 9, 13 is
    A) 2 B) 3 C) 4 D) 5
  4. The 5th term of AP: 2, 4, 6,…
    A) 8 B) 10 C) 12 D) 14
  5. Which is a GP?
    A) 2,4,6 B) 3,9,27 C) 5,10,15 D) 1,3,5
  6. Common ratio of 2, 6, 18
    A) 2 B) 3 C) 4 D) 5
  7. nth term of AP with a=3, d=2
    A) 3n B) 2n+1 C) 3+2n D) 3+2(n−1)
  8. Recursive rule means
    A) Direct formula
    B) Term depends on previous
    C) Only addition
    D) Only multiplication
  9. Sequence 1, 1, 2, 3, 5 is
    A) AP B) GP C) Fibonacci type D) None
  10. Sum of first 5 natural numbers
    A) 10 B) 15 C) 20 D) 25


👉 Sequences are everywhere — from mobile patterns to coding logic!

🔹 Questions 11–20

  1. Find 10th term of AP: 1,3,5,…
    A) 19 B) 20 C) 21 D) 18
  2. In GP, ratio is
    A) Difference B) Sum C) Division D) Product
  3. 2,6,18,… is
    A) AP B) GP C) Neither D) Both
  4. Sum of first n natural numbers formula is
    A) n² B) n(n+1)/2 C) n³ D) n/2
  5. Which is recursive?
    A) aₙ = n²
    B) aₙ = aₙ₋₁ + 2
    C) aₙ = 2n
    D) None
  6. First term of AP is 5, d=3 → second term
    A) 6 B) 7 C) 8 D) 9
  7. GP example
    A) 1,2,4,8
    B) 2,4,6,8
    C) 3,6,9
    D) 5,7,9
  8. 7th term of AP: a=1, d=2
    A) 11 B) 12 C) 13 D) 14
  9. If r=1, GP becomes
    A) Constant B) Increasing C) Decreasing D) Zero
  10. Tower of Hanoi is related to
    A) AP B) GP C) Recursion D) None


👉 Always write formula first — it reduces mistakes!

🔹 Questions 21–30

  1. Find aₙ if a=2, d=3, n=4
    A) 11 B) 12 C) 13 D) 14
  2. GP term: a=3, r=2, n=3
    A) 12 B) 18 C) 24 D) 36
  3. Difference in AP is always
    A) Variable B) Constant C) Zero D) Infinite
  4. Ratio in GP is always
    A) Constant B) Increasing C) Decreasing D) Zero
  5. Sequence 5,5,5 is
    A) AP B) GP C) Both D) None
  6. Recursive rule example
    A) aₙ = n²
    B) aₙ = aₙ₋₁ × 2
    C) aₙ = 3n
    D) None
  7. Sum of first 10 natural numbers
    A) 45 B) 50 C) 55 D) 60
  8. Which grows faster?
    A) AP B) GP C) Both same D) None
  9. AP used in
    A) Interest
    B) Equal increments
    C) Multiplication
    D) None
  10. GP used in
    A) Population growth
    B) Subtraction
    C) Addition
    D) None


👉 AP = Linear growth
👉 GP = Exponential growth

🔹 Questions 31–40

  1. 3rd term of AP: 2,5,…
    A) 7 B) 8 C) 9 D) 10
  2. GP: 4,8,16 → r=?
    A) 2 B) 3 C) 4 D) 5
  3. Recursive sequence depends on
    A) Future
    B) Previous
    C) Random
    D) None
  4. Sum formula gives
    A) Single term
    B) Total
    C) Difference
    D) Ratio
  5. Tower of Hanoi moves follow
    A) AP B) GP C) 2ⁿ−1 D) n²
  6. If d=0, AP becomes
    A) Constant
    B) Increasing
    C) Decreasing
    D) None
  7. 1,4,9,16 is
    A) AP B) GP C) Squares D) None
  8. nth term helps to
    A) Find any term
    B) Sum
    C) Difference
    D) Ratio
  9. GP formula includes
    A) Addition
    B) Multiplication
    C) Division
    D) Both B & C
  10. Natural numbers sum always
    A) Odd
    B) Even
    C) Integer
    D) Fraction


👉 Master sequences = Master patterns = Crack exams faster 🚀

🔹 Questions 41–50

  1. AP: 10,7,4 → d=?
    A) −3 B) 3 C) −2 D) 2
  2. GP: 9,3,1 → r=?
    A) 1/3 B) 3 C) −3 D) 2
  3. 6th term AP: a=2,d=2
    A) 10 B) 12 C) 14 D) 16
  4. GP term formula
    A) a+(n−1)d
    B) arⁿ⁻¹
    C) n²
    D) n³
  5. Recursive formula example
    A) aₙ = aₙ₋₁ + 1
    B) aₙ = n+1
    C) aₙ = 2n
    D) None
  6. Sequence pattern means
    A) Random
    B) Ordered rule
    C) No logic
    D) None
  7. AP real-life example
    A) Salary increase
    B) Virus spread
    C) Radioactivity
    D) None
  8. GP real-life example
    A) Savings
    B) Growth
    C) Decay
    D) All
  9. Fractals use
    A) AP
    B) GP
    C) Recursion
    D) Both B & C
  10. Tower of Hanoi minimum moves for n disks
    A) n²
    B) 2ⁿ−1
    C) n
    D) n³

🔹 Questions 51–60

  1. The common difference of the sequence 1/3x, (1−3x)/3x, (1−6x)/3x is
    A) 1 B) -1 C) x D) -x
  2. If the common difference of an AP is 5, then a18 − a13 =
    A) 5 B) 20 C) 25 D) 30
  3. The common difference of an AP where an = 3n + 7 is
    A) 3 B) 7 C) 10 D) 1
  4. If x+2, 2x, 2x+3 are in AP, then x =
    A) 3 B) 4 C) 5 D) 6
  5. The 10th term from the end of AP 4, 9, 14, …, 254 is
    A) 209 B) 204 C) 199 D) 194
  6. If 2y−1, 3y+5, 5y+1 are in AP, then y =
    A) -3 B) 4 C) 5 D) 2
  7. If a = -5 and d = 2, then sum of first 6 terms is
    A) 0 B) 5 C) 6 D) 15
  8. If a = 1, an = 20 and Sn = 399, then n =
    A) 19 B) 21 C) 38 D) 42
  9. The sum of first n odd natural numbers is
    A) 2n – 1 B) 2n + 1 C) n² D) n² – 1
  10. If Sn = 3n² + n, then common difference is
    A) 3 B) 6 C) 9 D) 1

🔹 Questions 61–70

  1. The formula an = Sn − Sn−1 is valid for
    A) n > 1 B) n = 1 C) all n D) n > 2
  2. If 5, k, 11 are in AP, then k =
    A) 7 B) 8 C) 9 D) 6
  3. Next term of sequence √2, √8, √18, √32 is
    A) √40 B) √48 C) √50 D) √60
  4. If a2 = 13 and a5 = 25, then a7 =
    A) 30 B) 33 C) 37 D) 38
  5. Number of two-digit numbers divisible by 3 is
    A) 25 B) 30 C) 32 D) 33
  6. If Sn = 2n² + 5n, then an =
    A) 4n + 3 B) 4n – 3 C) 3n + 4 D) 3n – 4
  7. If a, b, c are in AP, then (a − c)/(b − a) =
    A) 1 B) 2 C) -2 D) 0
  8. Sum of all two-digit odd numbers is
    A) 2475 B) 2530 C) 4905 D) 5049
  9. If d = -4, n = 7 and an = 4, then a =
    A) 6 B) 7 C) 20 D) 28
  10. The 10th term of AP 5, 8, 11 is
    A) 32 B) 35 C) 38 D) 185

🔹 Questions 71–80

  1. If common difference is d, then an − a(n−k) =
    A) (n−k)d B) kd C) n+kd D) nd
  2. Which term of AP 21, 18, 15 becomes 0
    A) 6th B) 7th C) 8th D) 9th
  3. Sum of first five multiples of 3 is
    A) 45 B) 55 C) 65 D) 75
  4. If a7 = 34 and a13 = 64, then a18 =
    A) 87 B) 88 C) 89 D) 90
  5. S(n+3) − 3S(n+2) + 3S(n+1) − Sn =
    A) 0 B) 1 C) d D) 2d
  6. Sum of first 100 natural numbers is
    A) 5050 B) 5000 C) 5150 D) 5005
  7. Special AP sum result is
    A) ab/(b−a)
    B) 3ab/2(b−a)
    C) 3a²/2(b−a)
    D) None
  8. Number of terms in AP 7, 13, 19, …, 205 is
    A) 33 B) 34 C) 35 D) 36
  9. If pth term is q and qth term is p, then nth term is
    A) p + q − n B) p − q + n C) q − p + n D) p + q + n
  10. Common difference of sequence 1/p, (1−p)/p is
    A) p B) -p C) -1 D) 1

🔹 Questions 81–90

  1. If Sn = n²p, then Sr =
    A) r²p B) rp² C) r³p D) mnp
  2. Sum of first n even numbers is
    A) n(n+1) B) n² C) n(n−1) D) 2n(n+1)
  3. If 4/5, a, 2 are in AP, then a =
    A) 7/5 B) 6/5 C) 9/5 D) 1
  4. If d = 0, then an =
    A) 0 B) 3.5 C) 103.5 D) 104.5
  5. If Sn = 3n² + 5n and am = 164, then m =
    A) 26 B) 27 C) 28 D) 25
  6. nth term of AP is
    A) a + nd B) a + (n−1)d C) a + (n+1)d D) nd
  7. If 18, a, b, -3 are in AP, then a + b =
    A) 19 B) 7 C) 11 D) 15
  8. Middle term of AP 10, 7, 4, …, -62 is
    A) -26 B) -25 C) -24 D) -23
  9. Common difference from sums is
    A) Sn − 2S(n−1) + S(n−2)
    B) Sn − S(n−1)
    C) Sn − S(n−2)
    D) Sn − 2S(n−1)
  10. Sum of odd numbers between 2 and 100 is
    A) 2499 B) 2500 C) 2475 D) 2525

🔹 Questions 91–100 (GP)

  1. nth term of GP is
    A) ar^n B) ar^(n−1) C) ar^(n+1) D) (ar)^(n−1)
  2. If a, b, c are in GP, then
    A) b = (a+c)/2 B) b² = ac C) 2b = a+c D) b = ac
  3. Common ratio of 2, 6, 18 is
    A) 2 B) 3 C) 4 D) 6
  4. 5th term when a = 2, r = 3 is
    A) 162 B) 486 C) 54 D) 108
  5. Middle term relation in GP is
    A) pq B) √pq C) p/q D) (p+q)/2
  6. Sum of infinite GP is
    A) a/(1 − r) B) a/(r − 1) C) a(1 − rⁿ)/(1 − r) D) ar/(1 − r)
  7. If x, x+3, x+9 are in GP, then x =
    A) 3 B) -3 C) 9 D) 27
  8. If 3rd term = 24 and 6th term = 192, then r =
    A) 2 B) 3 C) 4 D) 8
  9. Relation of P² is
    A) S/R B) R/S C) (S/R)^n D) (R/S)^n
  10. Product of first 5 terms when 3rd term is 4 is
    A) 4³ B) 4⁴ C) 4⁵ D) None

✅ Answers (1–100)

1-B, 2-B, 3-C, 4-B, 5-B, 6-B, 7-D, 8-B, 9-C, 10-B
11-A, 12-C, 13-B, 14-B, 15-B, 16-C, 17-A, 18-C, 19-A, 20-C
21-A, 22-A, 23-B, 24-A, 25-C, 26-B, 27-C, 28-B, 29-B, 30-A
31-B, 32-A, 33-B, 34-B, 35-C, 36-A, 37-C, 38-A, 39-D, 40-C
41-A, 42-A, 43-B, 44-B, 45-A, 46-B, 47-A, 48-D, 49-D, 50-B

51-B, 52-C, 53-A, 54-C, 55-A, 56-C, 57-A, 58-C, 59-C, 60-B
61-A, 62-B, 63-C, 64-B, 65-B, 66-A, 67-A, 68-A, 69-D, 70-A
71-B, 72-C, 73-A, 74-C, 75-A, 76-A, 77-B, 78-B, 79-A, 80-C
81-A, 82-A, 83-A, 84-B, 85-B, 86-B, 87-D, 88-A, 89-A, 90-B
91-B, 92-B, 93-B, 94-A, 95-B, 96-A, 97-A, 98-A, 99-C, 100-C

✅ FAQs

Q1. What is the difference between AP and GP?
AP has constant difference, GP has constant ratio.

Q2. Is Tower of Hanoi in syllabus?
Yes, it is included for understanding recursion.

Q3. How many formulas are in this chapter?
Around 5–10 important formulas are enough.

Q4. Which is more important AP or GP?
Both are equally important for exams.

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