NBT NBT Mathematics: Sequences, Series and Patterns 2

Question 1

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

Accepted Answer

10th

Answer

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?

Accepted Answer

3

Answer

T₆/T₃ = r³ = 486/18 = 27, so r = 3.

Question 3

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

Accepted Answer

15

Answer

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?

Accepted Answer

2186

Answer

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?

Accepted Answer

4

Answer

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

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