NBT Mathematics: Sequences, Series and Patterns Flashcards

If Tₙ = 4n − 3, which term of the sequence equals 37?

Answer: 10th

4n − 3 = 37 → 4n = 40 → n = 10, so it is the 10th term.

The 3rd term of a geometric sequence is 18 and the 6th term is 486. What is the common ratio?

Answer: 3

T₆/T₃ = r³ = 486/18 = 27, so r = 3.

How many terms are in the arithmetic sequence 7, 13, 19, …, 91?

Answer: 15

Tₙ = 7 + (n−1)6 = 91 → (n−1)6 = 84 → n−1 = 14 → n = 15.

What is the sum of the geometric series 2 + 6 + 18 + … + 1458?

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.

The general term of a quadratic sequence is Tₙ = 2n² − n + 1. What is the 2nd difference?

Answer: 4

For Tₙ = an², the 2nd difference is 2a = 2(2) = 4.

A sequence begins: 3, 6, 12, 24, … What is the ratio of T₈ to T₅?

Answer: 8

r = 2; T₈/T₅ = r³ = 2³ = 8.

Evaluate: ∑ₙ₌₁⁴ 3ⁿ

Answer: 120

3¹ + 3² + 3³ + 3⁴ = 3 + 9 + 27 + 81 = 120.