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Common Core Standard HSF-BF.A.2 Questions

Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.★

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Grade 11 Functions and Relations CCSS: HSF-BF.A.2
A worker earns $200 in the first week and an additional $50 each subsequent week. Which explicit formula represents their earnings after n weeks?
  1. an=200+50n
  2. an=20+200n
  3. an=200+50(n-1)
  4. an=50+200(n-1)
Grade 11 Functions and Relations CCSS: HSF-BF.A.2
A car depreciates by 15% annually. If its initial value is $20,000, which explicit formula models its value after n years?
  1. an=20,000·(0.15)n
  2. an=20,000·(0.85)n-1
  3. an=20,000·(0.85)n
  4. an=20,000-0.15n
Grade 10 Sequences and Series CCSS: HSF-BF.A.1, HSF-BF.A.1a, HSF-BF.A.2
Given the sequence defined by a(n)=3+5⋅2n, n∈ℕ,n≥1, which of the following recursive formulas defines the same sequence? Assume for all sequences that n∈ℕ.
  1. t(1)=13;  t(n)=3+5⋅2n-1,n>1
  2. t(1)=13;  t(n)=2t(n-1), n>1
  3. t(1)=13;  t(n)=13+t(n-1), n>1
  4. t(1)=13;  t(n)=-3+2t(n-1), n>1
Grade 9 Sequences and Series CCSS: HSF-BF.A.2
For the sequence defined by a1=4;  an=an-1-4,n>1, which of the following describes the same sequence? There may be more than one correct answer.
  1. an=8-4n
  2. an=4-4(n-1)
  3. an=4-4n
  4. an=-4-4(n-3)
Grade 11 Functions and Relations CCSS: HSF-BF.A.2
An arithmetic sequence has the explicit formula: an=−5+4n
What is the recursive formula?
  1. a₁=−5;an=an-1+4
  2. a₁=−1;an=an-1+4
  3. a₁=4;an=an-1-5
  4. a₁=−5;an=an-1-4
Grade 11 Functions and Relations CCSS: HSF-BF.A.2
What transformation occurs when replacing f(x) with f(x)+5?
  1. Shift left by 5 units
  2. Shift right by 5 units
  3. Shift up by 5 units
  4. Shift down by 5 units
Grade 10 Sequences and Series CCSS: HSF-BF.A.1, HSF-BF.A.1a, HSF-BF.A.2, HSF-LE.A.2
Which of the following recursive functions defines the sequence 5,8,11,14,...? Assume n∈ℕ.
  1. t(1)=3;  t(n)=t(n-1)+5, n>1
  2. t(1)=5,  t(n)=t(n-1)-3, n>1
  3. t(1)=5,  t(n)=t(n-1)+3, n>1
  4. t(2)=8,  t(n)=t(n-2)+6, n>2
Grade 10 Sequences and Series CCSS: HSF-BF.A.2
For the geometric sequence defined by an=3⋅2n-1, what is its recursive formula?
  1. a1=1;  an=2an-1, n>1
  2. a1=3;  an=2an-1, n>1
  3. a1=1;  an=3an-1, n>1
  4. a1=2;  an=3an-1, n>1
Grade 11 Functions and Relations CCSS: HSF-BF.A.2
Given the arithmetic sequence: 11, 8, 5, 2, … what is the recursive formula?
  1. a1=11;an=an-1−3
  2. a1=11;an=an-1+3
  3. a1=2;an=an-1−3
  4. a1=8;an=an-1−11
Grade 10 Sequences and Series CCSS: HSF-BF.A.1, HSF-BF.A.1a, HSF-BF.A.2, HSF-LE.A.2
Given the sequence 1,4,16,64,256,..., which of the following correctly defines this sequence in a recursive form? Assume that n∈ℕ.
  1. t(1)=1;  t(n)=4t(n-1), n>1
  2. t(1)=4;  t(n)=4t(n-1), n>1
  3. t(1)=1;  t(n)=14t(n-1), n>1
  4. t(1)=1;  t(n)=22(n-1),n>1
Grade 10 Sequences and Series CCSS: HSF-BF.A.2
If the explicit form of geometric sequence is an=4n, what is its recursive form?
  1. a1=0;  an=4an-1,n>1
  2. a1=1;  an=4an-1, n>1
  3. a1=4;  an=4n an-1, n>1
  4. a1=4;  an=4an-1, n>1
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