Class 9 Maths Predicting What Comes Next: Exploring Sequences and Progressions

A sequence is a list of numbers in a specific order.

👉 Example: 2, 4, 6, 8, 10…


📌 2. Pattern in Sequences

Patterns help us predict next terms.

Example:

  • 3, 6, 9, 12 → +3 pattern

📌 3. Arithmetic Progression (AP)

A sequence where difference between consecutive terms is constant.

👉 This constant is called common difference (d)


📌 4. General Form of AP

👉 a, a + d, a + 2d, a + 3d, …


📌 5. nth Term of AP

👉 aₙ = a + (n − 1)d


📌 6. Examples

  • 5, 10, 15, 20 → AP (d = 5)
  • 2, 5, 8, 11 → AP (d = 3)

CBSE MOCK TEST (100 QUESTIONS)

📘 Patterns, Sequences & Arithmetic Progression (AP)


🔹 SECTION A: MCQs (1–70)

1. A sequence is:
A) random numbers B) ordered numbers C) letters D) equations
Ans: B

2. Arithmetic progression has:
A) random difference B) no pattern C) constant difference D) multiplication pattern
Ans: C

3. Common difference is:
A) sum of terms B) product C) difference between terms D) quotient
Ans: C

4. AP stands for:
A) Algebraic Pattern B) Arithmetic Progression C) Average Problem D) Axis Point
Ans: B

5. First term of AP is denoted by:
A) d B) n C) a D) t
Ans: C


6. nth term of AP is:
A) a + nd B) a + (n−1)d C) nd + a² D) a/n
Ans: B

7. Sequence 2,4,6,8 is:
A) AP B) GP C) random D) none
Ans: A

8. Common difference of 3,6,9,12 is:
A) 1 B) 2 C) 3 D) 4
Ans: C

9. Sequence 5,10,15,20 is:
A) AP B) GP C) constant D) none
Ans: A

10. Next term of 7,14,21,28 is:
A) 30 B) 32 C) 35 D) 36
Ans: C


11. In AP, difference is:
A) changing B) constant C) zero always D) negative always
Ans: B

12. 1st term + (n−1)d gives:
A) sum B) nth term C) difference D) product
Ans: B

13. AP: 10, 20, 30, d =
A) 5 B) 10 C) 15 D) 20
Ans: B

14. AP: 100, 90, 80, d =
A) 10 B) −10 C) 20 D) −20
Ans: B

15. A sequence is AP if:
A) difference same B) product same C) ratio same D) random
Ans: A


16. 4th term of AP 3,6,9 is:
A) 9 B) 12 C) 15 D) 18
Ans: B

17. 5th term of 2,4,6 is:
A) 8 B) 10 C) 12 D) 14
Ans: B

18. d in AP 1,3,5 is:
A) 1 B) 2 C) 3 D) 4
Ans: B

19. AP starts with:
A) last term B) middle C) first term D) random
Ans: C

20. Pattern 2,4,8,16 is:
A) AP B) GP C) linear D) none
Ans: B


📝 SECTION B: ASSERTION–REASON (71–85)

A: Both true, R explains A
B: Both true, R not explanation
C: A true, R false
D: A false, R true


71. A: AP has constant difference
R: Difference between terms is same
Ans: A

72. A: nth term is a + nd
R: Formula is incorrect
Ans: D

73. A: 2,4,6 is AP
R: Difference is constant
Ans: A

74. A: 5,10,20 is AP
R: Ratio is constant
Ans: D

75. A: Sequence is ordered list
R: Order matters in sequences
Ans: A


📊 SECTION C: NUMERICALS (86–95)

86. Find next term: 3,6,9,12 →
👉 15

87. d of 20,15,10 →
👉 −5

88. 6th term of 2,4,6 →
👉 12

89. 10th term of AP 1,3,5 →
👉 19

90. Next term: 5,10,15 →
👉 20


91. Find d: 7,14,21 →
👉 7

92. 4th term of 10,20,30 →
👉 40

93. 3rd term of AP 5,8,11 →
👉 11

94. Find missing term: 2,__, 6,8 →
👉 4

95. 5th term of 1,2,3 →
👉 5


📄 SECTION D: VERY SHORT ANSWERS (96–100)

96. Define sequence
👉 Ordered numbers

97. Define AP
👉 Constant difference sequence

98. What is common difference?
👉 Difference between terms

99. Formula of nth term
👉 a + (n−1)d

100. Example of AP
👉 2,4,6,8