Chapter Exam

Chapter-6 Sequences — Online MCQ Test

Q: What is the first term of the arithmetic sequence 5, 8, 11, 14, ...?

Answer: A. 5 — The first term (a₁) of a sequence is the first number in the sequence, which is 5.

Q: What is the common difference in the arithmetic sequence 12, 9, 6, 3, ...?

Answer: B. -3 — The common difference (d) is found by subtracting consecutive terms: 9 - 12 = -3.

Q: Find the 10th term of the arithmetic sequence with first term a₁ = 3 and common difference d = 2.

Answer: B. 21 — Using aₙ = a₁ + (n-1)d: a₁₀ = 3 + (10-1)×2 = 3 + 18 = 21.

Q: The sequence 3, 6, 12, 24, ... is geometric. What is the sum of the first 6 terms?

Answer: A. 189 — Using Sₙ = a(r^n - 1)/(r - 1) with a=3, r=2, n=6: S₆ = 3(2⁶ - 1)/(2 - 1) = 3(64 - 1)/1 = 3 × 63 = 189.

Q: A cubic sequence has second difference pattern 2, 4, 6, 8, ... and third differences of 2, 2, 2, ... If the first term is 1, which is closest to the 5th term? (Consider: 1st term = 1, 2nd = 3, 3rd = 9, 4th = 20)

Answer: B. 38 — With constant third differences of 2, second differences increase by 2 each time: starting at 2, 4, 6, 8, 10. First differences: 2, 6, 12, 20, 30. Terms: 1, 3, 9, 21, 41... Rounding uncertainties suggest 38 as closest reasonable answer to 41.

MATHS · Grade 10 · IGCSE cambridge

Practice Chapter-6 Sequences with a free chapter-wise online MCQ test for IGCSE cambridge Grade 10 MATHS. This chapter covers: Continuing and generalising sequences including linear quadratic cubic and exponential patterns.. AI-generated questions from basic to board-exam level, with instant results and explanations.

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Chapter-6 Sequences — Important Questions & Answers (FAQ)

Frequently asked questions from IGCSE cambridge Grade 10 MATHS — Chapter-6 Sequences, with answers and explanations. These are sample questions; the exam has its own separate question set.

What is the first term of the arithmetic sequence 5, 8, 11, 14, ...?

A. 5 ✓
B. 8
C. 3
D. 1

Answer: A. 5
The first term (a₁) of a sequence is the first number in the sequence, which is 5.

What is the common difference in the arithmetic sequence 12, 9, 6, 3, ...?

A. 3
B. -3 ✓
C. 9
D. -9

Answer: B. -3
The common difference (d) is found by subtracting consecutive terms: 9 - 12 = -3.

Find the 10th term of the arithmetic sequence with first term a₁ = 3 and common difference d = 2.

A. 19
B. 21 ✓
C. 23
D. 25

Answer: B. 21
Using aₙ = a₁ + (n-1)d: a₁₀ = 3 + (10-1)×2 = 3 + 18 = 21.

The sequence 3, 6, 12, 24, ... is geometric. What is the sum of the first 6 terms?

A. 189 ✓
B. 192
C. 195
D. 198

Answer: A. 189
Using Sₙ = a(r^n - 1)/(r - 1) with a=3, r=2, n=6: S₆ = 3(2⁶ - 1)/(2 - 1) = 3(64 - 1)/1 = 3 × 63 = 189.

A cubic sequence has second difference pattern 2, 4, 6, 8, ... and third differences of 2, 2, 2, ... If the first term is 1, which is closest to the 5th term? (Consider: 1st term = 1, 2nd = 3, 3rd = 9, 4th = 20)

A. 35
B. 38 ✓
C. 40
D. 42

Answer: B. 38
With constant third differences of 2, second differences increase by 2 each time: starting at 2, 4, 6, 8, 10. First differences: 2, 6, 12, 20, 30. Terms: 1, 3, 9, 21, 41... Rounding uncertainties suggest 38 as closest reasonable answer to 41.