NBT Mathematics: Sequences, Series and Patterns Flashcards

The first three terms of an arithmetic sequence are 5, 11, 17. What is the 20th term?

Answer: 119

The common difference is 6, so the 20th term = 5 + (19)(6) = 5 + 114 = 119.

A geometric sequence has first term 4 and common ratio 3. What is the 5th term?

Answer: 324

T₅ = 4 × 3⁴ = 4 × 81 = 324.

What is the sum of the first 10 terms of the arithmetic series 3 + 7 + 11 + …?

Answer: 210

Sₙ = n/2 × (2a + (n−1)d) = 10/2 × (6 + 36) = 5 × 42 = 210.

Which formula gives the nth term of the sequence 2, 5, 10, 17, 26, …?

Answer: Tₙ = n² + 1

Each term equals n² + 1: T₁=2, T₂=5, T₃=10, T₄=17, T₅=26.

The sum of an infinite geometric series is 40 and its first term is 10. What is the common ratio?

Answer: 0.75

S∞ = a/(1−r) → 40 = 10/(1−r) → 1−r = 0.25 → r = 0.75.

A sequence is defined recursively as T₁ = 3 and Tₙ = Tₙ₋₁ + 4. What is T₆?

Answer: 23

Each term adds 4: 3, 7, 11, 15, 19, 23 — so T₆ = 23.

Evaluate: ∑ₖ₌₁⁵ (2k − 1)

Answer: 25

The terms are 1 + 3 + 5 + 7 + 9 = 25.