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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
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
Grade 11 Functions and Relations CCSS: HSF-BF.A.2
An arithmetic sequence has a3=20 and a6=38. What is the recursive formula?
  1. a1=8;an=an−1+6
  2. a1=6;an=an−1+8
  3. a1=14;an=an−1+6
  4. a1=20;an=an−1+9
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
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