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Common Core Standard HSF-IF.A.3 Questions

Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ≥ 1.

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Grade 10 Sequences and Series CCSS: HSF-IF.A.3
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]
Grade 9 Sequences and Series CCSS: HSF-IF.A.3
Find the next three terms for the sequence. [math] 14,34,54,74,94,...[/math]
  1. 114, 134, 154
  2. 188, 208, 228
  3. 104, 124, 144
  4. 84, 104, 124
Grade 10 Sequences and Series CCSS: HSF-IF.A.3
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.
Grade 9 Sequences and Series CCSS: HSF-IF.A.3
Grade 9 Sequences and Series CCSS: HSF-IF.A.3
Grade 10 Sequences and Series CCSS: HSF-IF.A.3
Grade 11 Sequences and Series CCSS: HSF-IF.A.3
Find the next three terms in this sequence: 5120, 1280, 320, 80...
  1. -160, -400, -640
  2. 20, 5, 1.25
  3. 40, 20, 10
  4. 76, 72, 68
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