Sequence Study Guide

45, 38, 31, 24, 17, ...

Which function defines the nth term of the sequence?

• A(n) = 52 – 7n

• A(n) = 45 – 7n

• A(n) = 46 – n

• A(n) = 52 + 7n

The explicit formula below describes a linear function, where n is a positive integer.

f(n) = 3n – 8

Which recursive formula describes the same function?

• a₁ = -5

  a_n = a_n-1 + 3

• a₁ = 3

  a_n = a_n-1 – 8

• a₁ = -8

  a_n = a_n-1 + 3

• a₁ = 3

  a_n = a_n-1 - 5

The first five terms of a sequence are listed below.

3, 7, 11, 15, 19, ...

Which of the following definitions, either explicit or recursive, correctly describes the n term of the sequence? Select all that apply. (Pick two)

• f(n)=3+4n

• ƒ(n) = 3 + 4(n – 1)

• ƒ(n) = 4 + 3(n – 1)

• ƒ(1) = 3

  ƒ(n) = 4ƒ(n – 1)

• ƒ(1) = 3

  ƒ(n)= ƒ(n – 1) + 4

Consider the following sequence, f(n) = 3, 6, 12, 24, ..., where f(n) represents the sequence.

Which of the following notations represent correct interpretations that can be made about the sequence? Select the three that apply. Pick up to 3 answers

• f(5) = 48

• f(8) = 24

• f(n) = 3(2)^n-1

• f(n) = 2f(n – 1)

• f(11) = 3 + (10)2

Given the recursive function below

a₁=3

a_n= -2a_n-1

What are the first 4 terms of the sequence?

• 3, -6, 12, -24

• 3, 6, 12, 24

• -2, -6, -18, -32

• 1, -2, 3, 4

What is the 10th term of the geometric sequence below?

7, –14, 28, –56, ...

• 3584

• -3584

• 7168

• -7168

Given the table identify the correct explicit formula.

• S(n) = 40,000(1.05)ⁿ

• S(n) = 40,000 + 1.05n

• S(n) = 40,000(1.05)^n-1

• S(n) = 40,000 + 1.05(n – 1)

The function below models a book fine, in dollars, that a certain library charges for a book that is n days overdue.

f(n) = 0.50 + 0.25(n – 1)

What is the value of the 10 term of the sequence generated by the function f(n) ?

• $2.00

• $2.50

• $2.75

• $3.00

Marlene wrote an arithmetic sequence where a = 8 and the common difference is –3.

What is a rule for the nth term of this sequence?

• a_n=8n-3

• a_n=11n-3

• a_n=-3n+8

• a_n=-3n+11

Given h(x) = 3x – 3, solve for x when h(x) = 0.

• x=3

• x= -3

• x=1

• x= -1