Sequences as Functions (Grade 10)
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Sequences as Functions
1.
Which function describes the sequence [math]3, 7, 11...[/math]?
- [math]f(n)=4n-1[/math]
- [math]f(n)=3+2n[/math]
- [math]f(x)=2n-3[/math]
- [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?
- [math]f(n)=6n+16[/math]
- [math]f(n)=6n-2[/math]
- [math]f(x)=3x+12[/math]
- [math]f(x)=12x+6[/math]
3.
What is the explicit function of the geometric sequence 3, 4.5, 6.75, ...?
- [math]f(n)=1.5f(n-1)[/math] where [math]f(1)=3[/math]
- [math]f(n)=3*1.5^(n-1)[/math]
- [math]f(n)=1.5*3^(n-1)[/math]
- [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?
- [math]f(n) = 3*2^(n-1), n>=2[/math]
- [math]f(n) = 3*2^(n-1), n>=1[/math]
- [math]f(n) = 3*2^n, n>=1[/math]
- [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?
- -4
- 30
- 26
- 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.
- [math]ZZ^+[/math]
- [math]RR[/math]
- [math]{8, 13, 18,...}[/math]
- [math]{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.
- [math]RR[/math]
- [math]ZZ[/math]
- [math]ZZ^+[/math]
- [math]{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.
- [math]RR[/math]
- [math]ZZ^+[/math]
- [math]{n in ZZ^+ | n >=2}[/math]
- [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?
- Yes, these are the same sequences.
- No, the second sequence doesn't define its second term, and therefore isn't complete.
- No, they have different recursive relationships.
- 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.
- 90.5
- 64
- 128
- This value cannot be evaluated for this function, since it is not in the domain.
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