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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 10 Sequences and Series CCSS: HSF-BF.A.1, HSF-BF.A.1a, HSF-BF.A.2, HSF-LE.A.2
Find the recursive form of the sequence 10,5,0,-5,-10,... Assume n∈ℕ.
  1. t(1)=10;  t(n)=-t(n-1)+5, n>1
  2. t(1)=10;  t(n)=-5+t(n-1), n>1.
  3. t(1)=10;  t(n)=10-t(n-1), n>1.
  4. t(1)=10;  t(n)=t(n-1)-5,n>1
Grade 10 Sequences and Series CCSS: HSF-BF.A.2
What is the recursive form of the the geometric sequence defined by an=-5⋅3n-1?
  1. a1=-5;  an=3an-1, n>1
  2. a1=-15;  an=3an-1, n>1
  3. a1=3;  an=-5an-1, n>1
  4. a1=1;  an=5an-1, n>1
Grade 11 Functions and Relations CCSS: HSF-BF.A.2
A geometric sequence has the explicit formula: an=3·5ⁿ⁻¹
What is the recursive formula?
  1. a₁=3;an=5·an-1
  2. a₁=5;an=3·an-1
  3. a₁=1;an=5·an-1
  4. a₁=15;an=3·an-1
Grade 11 Functions and Relations CCSS: HSF-BF.A.2
For the sequence defined by the explicit formula an=5+2n, what is the recursive formula?
  1. a1=5;an=an−1+2,n>1
  2. a1=7;an=an−1+2,n>1
  3. a1=2;an=an−1+5,n>1
  4. a1=0;an=an−1+5,n>1
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 128,64,32,16,8,... which of the following functions describes it? Assume n∈ℕ.
  1. t(1)=128;  t(n)=2t(n-1), n>1
  2. t(1)=128;  t(n)=128-t(n-1), n>1
  3. t(1)=128;  t(n)=t(n)-12t(n-1),n>1
  4. t(1)=128;  t(n)=12t(n-1), n>1
Grade 10 Sequences and Series CCSS: HSF-BF.A.2
Given the geometric sequence defined by an=18⋅8n, what is the recursive form of this sequence?
  1. a1=1;  an=8an-1, n>1
  2. a1=18;  an=8an-1, n>1
  3. a1=8;  an=8an-1, n>1
  4. a1=8;  an=18an-1, n>1
Grade 11 Functions and Relations CCSS: HSF-BF.A.2
A car’s value decreases by 1,500 each year. If its initial value is 20,000, which explicit formula models its value after n years?
  1. an=20,000−1,500n
  2. an=20,000+1,500n
  3. an=1,500−20,000n
  4. an=1,500+20,000n
Grade 11 Functions and Relations CCSS: HSF-BF.A.2
For the sequence defined by an=12·4n-1, how could the same sequence be written recursively? (Select all that apply.)
  1. a1=12;an=4·an-1n>1
  2. a1=2;an=4·an-1n>1
  3. a1=12;an=2·an-14n>2
  4. a1=4;an=12·an-1n>1
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 functions describes the sequence 18,312,13,212,8,...? Assume that n∈ℕ.
  1. t(1)=18;  t(n)=4350t(n-1),n>1
  2. t(1)=18;  t(n)=t(n-1)-52,n>1
  3. t(1)=18;  t(n)=t(n-2)-5,n>2
  4. t(1)=18;  t(n)=52-t(n-1),t>1
Grade 10 Sequences and Series CCSS: HSF-BF.A.2
For the geometric sequence defined by an=14⋅(43)n, what is the recursive form of the this sequence?
  1. a1=1;  an=43an-1, n>1
  2. a1=14;  an=13an-1, n>1
  3. a1=14;  an=43an-1, n>1
  4. a1=13;  an=43an-1, n>1
Grade 11 Functions and Relations CCSS: HSF-BF.A.2
If an arithmetic sequence has the recursive formula a1=3;an=an-1−4, what is the explicit formula?
  1. an=3−4n
  2. an=7−4n
  3. an=1−4n
  4. an=3+4n
Grade 11 Functions and Relations CCSS: HSF-BF.A.2
Given the geometric sequence: 81, 27, 9, 3, … what is the explicit formula?
  1. an=81·(13)n-1
  2. an=27·(13)n-1
  3. an=81·3n-1
  4. an=3·81n-1
Grade 11 Functions and Relations CCSS: HSF-BF.A.2
A gym membership costs $40 initially, with a $5 monthly fee increase. Which recursive formula models the cost after n months?
  1. a1=40;an=an-1+5
  2. a1=45;an=an-1+5
  3. a1=40;an=an-1+40
  4. a1=5;an=an-1+40
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 functions correctly describe(s) the sequence 3,5,7,9,11,...? Assume that n∈ℕ. There may be more than one correct answer.
  1. t(1)=3;  t(n)=t(n-1)+2, n>1
  2. t(1)=3, t(2)=5;  t(n)=t(n-2)+4,n>2
  3. t(1)=3, t(2)=5;  t(n)=-t(n-1)+2t(n-2)+6, n>2
  4. t(1)=3;  t(n+1)=t(n)+2, n≥1
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