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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 9 Sequences and Series CCSS: HSF-BF.A.2
For the sequence defined by a1=3;  an=an-1+5, n>1, what is its explicit form?
  1. an=3-5n
  2. an=-2+5n
  3. an=5-3n
  4. an=1-2n
Grade 11 Functions and Relations CCSS: HSF-BF.A.2
A tree grows 8 inches per year. If it was 60 inches tall initially, which formula gives its height after n years?
  1. Recursive:a1=60;an=an-1+8
  2. Explicit: an=60.8n
  3. Recursive:a1=8;an=an-1+60
  4. Explicit: an=8+60n
Grade 11 Functions and Relations CCSS: HSF-BF.A.2
A car loses 10% of its value each year. If its initial value is $25,000, which explicit formula models its value after n years?
  1. an=25,000·(0.10)n
  2. an=25,000·(0.90)n-1
  3. an=25,000·(0.90)n
  4. an=25,000-0.10n
Grade 9 Sequences and Series CCSS: HSF-BF.A.2
Which of the following is the recursive formula for the geometric sequence 14,18,116,...?
  1. an=14⋅(12)n-1
  2. a1=12;an=(14)⋅an-1
  3. an=12⋅(14)n-1
  4. a1=14;an=(12)⋅an-1
Grade 9 Sequences and Series CCSS: HSF-BF.A.2
What is the explicit form of the sequence defined by a1=0;  an=an-1+3, n>1?
  1. an=3+3n
  2. an=3n
  3. an=-3+n
  4. an=-3+3n
Grade 11 Functions and Relations CCSS: HSF-BF.A.2
A ball bounces to half its previous height each time. If the first bounce reaches 32 cm, what is the explicit formula for the height after n bounces?
  1. an=32⋅(12)n
  2. an=32⋅(12)n-1
  3. an=12⋅(32)n-1
  4. an=32-(12)n
Grade 11 Functions and Relations CCSS: HSF-BF.A.2
A population of bacteria doubles every hour. If the initial population is 500, which recursive formula models the population after n hours?
  1. a₁=500;an=2·an-1n>1
  2. a₁=1,000;an=2·an-1n>1
  3. a₁=500;an=an-1+500n>1
  4. a₁=500;an=500·2n-1n>1
Grade 11 Functions and Relations CCSS: HSF-BF.A.2
An arithmetic sequence has a4=22 and a7=37. What is the recursive formula?
  1. a1=5;an=an-1+7
  2. a1=7;an=an-1+5
  3. a1=10;an=an-1+3
  4. a1=4;an=an-1+6
Grade 9 Sequences and Series CCSS: HSF-BF.A.2
Which of the following is the explicit formula for the arithmetic sequence -1, 1, 3, 5, ... ?
  1. an=-1+(n-1)⋅2
  2. an=-1⋅(2)n-1
  3. a1=-1;an=an-1+2
  4. an=2+(n-1)⋅(-1)
Grade 9 Sequences and Series CCSS: HSF-BF.A.2
Given the arithmetic sequence defined by a1=-10;  an=an-1+10, n>1, what is the explicit form of this sequence?
  1. an=10n
  2. an=-10+10n
  3. an=10-10n
  4. an=-20+10n
Grade 11 Functions and Relations CCSS: HSF-BF.A.2
For the sequence defined by an=5·3n-1, how could the same sequence be written recursively? (Select all that apply.)
  1. a1=5;an=3·an−1n>1
  2. a1=3;an=5·an−1n>1
  3. a1=15;an=3·an−1n>1
  4. a1=5,a2=2;an=3·an−1n>2
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