NBT NBT Mathematics: Sequences, Series and Patterns 3

Question 1

The 7th term of an arithmetic sequence is 43 and the common difference is 6. What is the first term?

Accepted Answer

7

Answer

T₇ = a + 6d = a + 36 = 43 → a = 7.

Question 2

For which value(s) of n does the series ∑ₖ₌₁ⁿ k = 55?

Accepted Answer

n = 10

Answer

Sₙ = n(n+1)/2 = 55 → n(n+1) = 110 → n = 10.

Question 3

A pattern of dots: Row 1 has 1 dot, Row 2 has 3, Row 3 has 5. How many dots are in Row n?

Accepted Answer

2n − 1

Answer

Each row adds 2 more dots; the nth row has 2n − 1 dots.

Question 4

A geometric series has S∞ = 12 and r = 1/3. What is the first term?

Accepted Answer

8

Answer

S∞ = a/(1−r) = a/(2/3) = 3a/2 = 12 → a = 8.

Question 5

The second differences of a sequence are all equal to 6. If T₁ = 2 and T₂ = 5, what is T₃?

Accepted Answer

14

Answer

First difference Δ₁ = T₂ − T₁ = 3; next first difference = 3 + 6 = 9; T₃ = 5 + 9 = 14.

(NBT) National Benchmark Test Practice Test