NBT NBT Mathematics: Sequences, Series and Patterns 1

Question 1

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

Accepted Answer

119

Answer

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?

Accepted Answer

324

Answer

T₅ = 4 × 3⁴ = 4 × 81 = 324.

Question 3

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

Accepted Answer

210

Answer

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, …?

Accepted Answer

Tₙ = n² + 1

Answer

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?

Accepted Answer

0.75

Answer

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

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