NBT NBT Mathematics: Sequences, Series and Patterns 4

Question 1

The sum of the first n terms of a series is given by Sₙ = 3n² − n. What is T₄?

Accepted Answer

20

Answer

T₄ = S₄ − S₃ = (3×16−4) − (3×9−3) = 44 − 24 = 20.

Question 2

A geometric sequence has T₂ = 6 and T₅ = 162. What is the first term?

Accepted Answer

2

Answer

T₅/T₂ = r³ = 162/6 = 27 → r = 3; T₁ = T₂/r = 6/3 = 2.

Question 3

How many terms of the series 8 + 11 + 14 + … are needed for the sum to first exceed 100?

Accepted Answer

7

Answer

Sₙ = n/2(16 + 3(n−1)) > 100. For n=7: S₇ = 7/2(37) = 129.5 > 100; S₆ = 3(32) = 96 < 100.

Question 4

Express 0.\overline{36} as a fraction in lowest terms.

Accepted Answer

4/11

Answer

0.363636… = 36/99 = 4/11.

Question 5

The nth term of a sequence is Tₙ = n(n + 2). Which of the following is NOT a term of this sequence?

Accepted Answer

10

Answer

Tₙ = n(n+2) gives 3, 8, 15, 24 for n=1,2,3,4. The value 10 is between T₂=8 and T₃=15 and cannot be produced.

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