NBT NBT Mathematics: Sequences, Series and Patterns 1 — Questions and Answers
Question 1: The first three terms of an arithmetic sequence are 5, 11, 17. What is the 20th term?
- 119 (Correct answer)
- 121
- 123
- 125
Correct answer: 119
The common difference is 6, so the 20th term = 5 + (19)(6) = 5 + 114 = 119.
Question 2: A geometric sequence has first term 4 and common ratio 3. What is the 5th term?
- 108
- 243
- 324 (Correct answer)
- 972
Correct answer: 324
T₅ = 4 × 3⁴ = 4 × 81 = 324.
Question 3: What is the sum of the first 10 terms of the arithmetic series 3 + 7 + 11 + …?
- 183
- 210 (Correct answer)
- 220
- 230
Correct answer: 210
Sₙ = n/2 × (2a + (n−1)d) = 10/2 × (6 + 36) = 5 × 42 = 210.
Question 4: Which formula gives the nth term of the sequence 2, 5, 10, 17, 26, …?
- Tₙ = n² + 1 (Correct answer)
- Tₙ = 2n + 1
- Tₙ = n² − 1
- Tₙ = 3n − 1
Correct answer: Tₙ = n² + 1
Each term equals n² + 1: T₁=2, T₂=5, T₃=10, T₄=17, T₅=26.
Question 5: The sum of an infinite geometric series is 40 and its first term is 10. What is the common ratio?
- 0.25
- 0.50
- 0.60
- 0.75 (Correct answer)
Correct answer: 0.75
S∞ = a/(1−r) → 40 = 10/(1−r) → 1−r = 0.25 → r = 0.75.
Question 6: A sequence is defined recursively as T₁ = 3 and Tₙ = Tₙ₋₁ + 4. What is T₆?
- 19
- 21
- 23 (Correct answer)
- 27
Correct answer: 23
Each term adds 4: 3, 7, 11, 15, 19, 23 — so T₆ = 23.
Question 7: Evaluate: ∑ₖ₌₁⁵ (2k − 1)
- 20
- 25 (Correct answer)
- 30
- 35
Correct answer: 25
The terms are 1 + 3 + 5 + 7 + 9 = 25.
NBT NBT Mathematics: Sequences, Series and Patterns 1
The first three terms of an arithmetic sequence are 5, 11, 17.
What is the 20th term?