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This printable supports Common Core Mathematics Standard HSF-BF.A.1, HSF-BF.A.1a

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Sequences as Recursive Functions (Grade 10)

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Sequences as Recursive Functions

Instructions: For these questions, the set [math]NN[/math] does not include zero.

1. 
Which of the following recursive functions defines the sequence [math]5,8,11,14,... ?[/math] Assume [math]n in NN[/math].
  1. [math]t(1) = 3; \ \ t(n) = t(n-1) + 5, \ n>1[/math]
  2. [math]t(1) = 5, \ \ t(n) = t(n-1) - 3, \ n>1[/math]
  3. [math]t(1) = 5, \ \ t(n) = t(n-1) + 3, \ n>1[/math]
  4. [math]t(2) = 8, \ \ t(n) = t(n-2) + 6, \ n>2[/math]
2. 
Given the sequence [math]1,4,16,64,256,...[/math], which of the following correctly defines this sequence in a recursive form? Assume that [math]n in NN[/math].
  1. [math]t(1) = 1; \ \ t(n) = 4t(n-1), \ n>1[/math]
  2. [math]t(1) = 4; \ \ t(n) = 4t(n-1), \ n>1[/math]
  3. [math]t(1) = 1; \ \ t(n) = 1/4 t(n-1), \ n>1[/math]
  4. [math]t(1) = 1; \ \ t(n) = 2^(2(n-1)), n>1[/math]
3. 
Find the recursive form of the sequence [math]10, 5, 0, -5, -10,...[/math] Assume [math]n in NN[/math].
  1. [math]t(1) = 10; \ \ t(n) = -t(n-1) + 5, \ n>1[/math]
  2. [math]t(1) = 10; \ \ t(n) = -5 + t(n-1), \ n>1[/math].
  3. [math]t(1) = 10; \ \ t(n) = 10 - t(n-1), \ n>1[/math].
  4. [math]t(1) = 10; \ \ t(n) = t(n-1) - 5, n>1[/math]
4. 
Given the sequence [math]128, 64, 32, 16, 8, ...[/math] which of the following functions describes it? Assume [math]n in NN[/math].
  1. [math]t(1) = 128; \ \ t(n) = 2 t(n-1), \ n>1[/math]
  2. [math]t(1) = 128; \ \ t(n) = 128 - t(n-1), \ n>1[/math]
  3. [math]t(1) = 128; \ \ t(n) = t(n) - 1/2t(n-1), n>1[/math]
  4. [math]t(1) = 128; \ \ t(n) = 1/2 t(n-1), \ n>1[/math]
5. 
Which of the following functions describes the sequence [math]18, 31/2, 13, 21/2, 8, ... ?[/math] Assume that [math]n in NN[/math].
  1. [math] t(1) = 18; \ \ t(n) = 43/50 t(n-1), n>1[/math]
  2. [math]t(1) = 18; \ \ t(n) = t(n-1) - 5/2, n>1[/math]
  3. [math]t(1) = 18; \ \ t(n) = t(n-2) - 5, n>2[/math]
  4. [math]t(1) = 18; \ \ t(n) = 5/2 - t(n-1), t>1[/math]
6. 
Which of the following functions correctly describe(s) the sequence [math]3,5,7,9,11,... ?[/math] Assume that [math]n in NN[/math]. There may be more than one correct answer.
  1. [math]t(1) = 3; \ \ t(n) = t(n-1) +2, \ n>1[/math]
  2. [math]t(1)=3, \ t(2)=5; \ \ t(n) = t(n-2) + 4, n>2[/math]
  3. [math]t(1) = 3, \ t(2) = 5; \ \ t(n) = -t(n-1) + 2t(n-2) + 6, \ n>2[/math]
  4. [math]t(1) = 3; \ \ t(n+1) = t(n) +2, \ n>=1[/math]
7. 
Which recursive function defines the sequence [math]0, 2, 2, 10, 18, 58, 130, ...[/math] for [math]n in N ?[/math]
  1. [math]t(1) = 0; \ \ t(n) = t(n-1) + n-2, \ n>1[/math]
  2. [math]t(1)=0, \ t(2)=2; \ \ t(n) = t(n-1) + 4t(n-2), \ n>2[/math]
  3. [math]t(1)=0, \ t(2)=2; \ \ t(n) = t(n-1) + 2t(n-2), \ n>2[/math]
  4. [math]t(1)=0, \ t(2)=2; \ \ t(n) = t(n-1) + 4(n-2), \ n>2[/math]
8. 
Given the sequence defined by [math]a(n) = 3 + 5*2^n, \ n in NN, n >=1[/math], which of the following recursive formulas defines the same sequence? Assume for all sequences that [math]n in NN[/math].
  1. [math]t(1) = 13; \ \ t(n) = 3 + 5*2^(n-1), n>1[/math]
  2. [math]t(1) = 13; \ \ t(n) = 2 t(n-1), \ n>1[/math]
  3. [math]t(1) = 13; \ \ t(n) = 13 + t(n-1), \ n>1[/math]
  4. [math]t(1) = 13; \ \ t(n) = -3 + 2t(n-1), \ n >1[/math]
9. 
Which of the following functions correctly describes the sequence [math]1,3,5,9,13,21,...?[/math] Assume that [math]n in NN[/math].
  1. [math] t(1) = 1, t(2) = 3; \ \ t(n) = 2t(n-2) + 3, n>2[/math]
  2. [math]t(1) = 1; \ \ t(n) = t(n-1) + 2, n>1[/math]
  3. [math]t(1)=1, t(2)=3; \ \ t(n) = t(n-2) + t(n-1) + 1, n>2[/math]
  4. [math]t(1) = 1; \ \ t(n) = t(n-1) + 2^(n-1), \ n>1[/math]
10. 
Given the sequence [math]1, -3, -9, -17, -27, ...[/math], which of the following functions correctly describes it? Assume that [math]n in NN[/math].
  1. [math]t(1) = 1, t(2) = -3; \ \ t(n) = t(n-1) - 6t(n-2), n>2[/math]
  2. [math]t(1) = 1; \ \ t(n) = t(n-1) -4, \ n>1[/math]
  3. [math]t(1) = 1; \ \ t(n) = t(n-1) - 2n, \ n > 1[/math]
  4. [math]t(1) = 1; \ \ t(n) = (-1)^(n-1) * 3 * t(n-1), n>1[/math]

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