NBT NBT Mathematics: Sequences, Series and Patterns 2 — Questions and Answers
Question 1: If Tₙ = 4n − 3, which term of the sequence equals 37?
- 9th
- 10th (Correct answer)
- 11th
- 12th
Correct answer: 10th
4n − 3 = 37 → 4n = 40 → n = 10, so it is the 10th term.
Question 2: The 3rd term of a geometric sequence is 18 and the 6th term is 486. What is the common ratio?
- 2
- 3 (Correct answer)
- 4
- 6
Correct answer: 3
T₆/T₃ = r³ = 486/18 = 27, so r = 3.
Question 3: How many terms are in the arithmetic sequence 7, 13, 19, …, 91?
- 13
- 14
- 15 (Correct answer)
- 16
Correct answer: 15
Tₙ = 7 + (n−1)6 = 91 → (n−1)6 = 84 → n−1 = 14 → n = 15.
Question 4: What is the sum of the geometric series 2 + 6 + 18 + … + 1458?
- 2184
- 2186 (Correct answer)
- 2188
- 2190
Correct answer: 2186
Number of terms: 2×3ⁿ⁻¹=1458 → 3ⁿ⁻¹=729 → n=7. Sₙ = 2(3⁷−1)/(3−1) = 2(2187−1)/2 = 2186.
Question 5: The general term of a quadratic sequence is Tₙ = 2n² − n + 1. What is the 2nd difference?
- 2
- 3
- 4 (Correct answer)
- 6
Correct answer: 4
For Tₙ = an², the 2nd difference is 2a = 2(2) = 4.
Question 6: A sequence begins: 3, 6, 12, 24, … What is the ratio of T₈ to T₅?
- 4
- 8 (Correct answer)
- 16
- 32
Correct answer: 8
r = 2; T₈/T₅ = r³ = 2³ = 8.
Question 7: Evaluate: ∑ₙ₌₁⁴ 3ⁿ
- 108
- 117
- 120 (Correct answer)
- 126
Correct answer: 120
3¹ + 3² + 3³ + 3⁴ = 3 + 9 + 27 + 81 = 120.
NBT NBT Mathematics: Sequences, Series and Patterns 2
If Tₙ = 4n − 3, which term of the sequence equals 37?