Sequences as Functions (Grade 10)

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Sequences as Functions

1. 
Which function describes the sequence [math]3, 7, 11...[/math]?
  1. [math]f(n)=4n-1[/math]
  2. [math]f(n)=3+2n[/math]
  3. [math]f(x)=2n-3[/math]
  4. [math]f(n)=4x-1[/math]
2. 
The third, fourth, and fifth numbers in a sequence are [math]16, 22, 28[/math]. Which function describes the sequence?
  1. [math]f(n)=6n+16[/math]
  2. [math]f(n)=6n-2[/math]
  3. [math]f(x)=3x+12[/math]
  4. [math]f(x)=12x+6[/math]
3. 
What is the explicit function of the geometric sequence 3, 4.5, 6.75, ...?
  1. [math]f(n)=1.5f(n-1)[/math] where [math]f(1)=3[/math]
  2. [math]f(n)=3*1.5^(n-1)[/math]
  3. [math]f(n)=1.5*3^(n-1)[/math]
  4. [math]f(n)=3f(n-1)[/math] where [math]f(1)=1.5[/math]
4. 
Given the recursive function [math]f(1) = 3; \ \ f(n) = 2 * f(n-1), n>=2[/math] for a geometric sequence, which of the following functions describes the same geometric sequence?
  1. [math]f(n) = 3*2^(n-1), n>=2[/math]
  2. [math]f(n) = 3*2^(n-1), n>=1[/math]
  3. [math]f(n) = 3*2^n, n>=1[/math]
  4. [math]f(n) = 3*2^n, n>=2[/math]
5. 
Given the arithmetic sequence defined by the function [math]f(n) = -4 + 3n[/math], what is the 10th term in this sequence?
  1. -4
  2. 30
  3. 26
  4. Not enough information.
6. 
Given the sequence [math]8, 13, 18, 23, ...[/math] what is the domain of the function [math]f(n) = 3+5n[/math] which describes this sequence? Note: [math]ZZ^+[/math] refers to the set of positive integers.
  1. [math]ZZ^+[/math]
  2. [math]RR[/math]
  3. [math]{8, 13, 18,...}[/math]
  4. [math]{n | n in ZZ, n >= 8}[/math]
7. 
For the geometric sequence [math]-1, 3, -9, 27, ...[/math] defined by the function [math]f(x) = -1*(-3)^(x-1)[/math], what is the domain of this function? Note: [math]ZZ^+[/math] refers to the set of positive integers.
  1. [math]RR[/math]
  2. [math]ZZ[/math]
  3. [math]ZZ^+[/math]
  4. [math]{x | x in ZZ, x!=0}[/math]
8. 
The Fibonacci sequence, 0, 1, 1, 2, 3, 5, 8,..., can be defined by the recursive function [math]f(0) = 0; f(1) = 1; f(n) = f(n-2) + f(n-1), n>=2[/math]. What is the domain of this function? Note: [math]NN[/math] refers to the natural numbers (the positive integers and zero), and [math]ZZ^+[/math] refers to the positive integers.
  1. [math]RR[/math]
  2. [math]ZZ^+[/math]
  3. [math]{n | n in ZZ^+, n >=2}[/math]
  4. [math]NN[/math]
9. 
A given arithmetic sequence is described by the function [math]f(1) = -8; \ \ f(n) = f(n-1) + 4, n>=2[/math]. Does the function [math]f(1) = -8; f(n) = f(n-2) + 8, n>=3[/math] describe the same sequence? If not, why?
  1. Yes, these are the same sequences.
  2. No, the second sequence doesn't define its second term, and therefore isn't complete.
  3. No, they have different recursive relationships.
  4. No, they have different domains.
10. 
A certain geometric sequence is defined by the function [math]f(x) = 512*(1/2)^(x-1), x in ZZ^+[/math], where [math]ZZ^+[/math] indicates the positive integers. What is the value of [math]f(3.5)? [/math] Round your answer to one decimal place, if necessary.
  1. 90.5
  2. 64
  3. 128
  4. This value cannot be evaluated for this function, since it is not in the domain.

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