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Tenth Grade (Grade 10) Sequences and Series Questions

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Grade 10 Sequences and Series CCSS: HSF-IF.A.3
What is the function that creates the sequence 14,15,17,21,29...?
  1. f(x)=10+52x
  2. f(x)=14+2x-1
  3. f(x)=15+3x+1
  4. f(x)=13+2x-1
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 10 Sequences and Series CCSS: HSF-BF.A.1, HSF-BF.A.1a, HSF-LE.A.2
Which recursive function defines the sequence 0,2,2,10,18,58,130,... for n∈N?
  1. t(1)=0;  t(n)=t(n-1)+n-2, n>1
  2. t(1)=0, t(2)=2;  t(n)=t(n-1)+4t(n-2), n>2
  3. t(1)=0, t(2)=2;  t(n)=t(n-1)+2t(n-2), n>2
  4. t(1)=0, t(2)=2;  t(n)=t(n-1)+4(n-2), 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 10 Sequences and Series CCSS: HSF-IF.A.3
What function expresses the sequence 3,24,243,3072,46875...?
  1. f(x)=(n+1)n⋅3
  2. f(x)=2xx-12
  3. f(x)=-4+5x+1
  4. f(x)=2xx+13
Grade 10 Sequences and Series CCSS: HSF-IF.A.3
Which of the following sequences shows answers to the function f(x)=2⋅3x?
  1. 4,8,16,32...
  2. 6,18,54,162...
  3. 12,24,48,96...
  4. 9,27,81,243...
Grade 10 Sequences and Series CCSS: HSF-BF.A.2
For the sequence defined by a1=100;  an=-15an-1, n>1, what is the explicit form of this sequence? There may be more than one correct answer.
  1. an=100⋅(-15)n-1
  2. an=-500⋅(-15)n
  3. an=100⋅(-15)n
  4. an=(-1)n⋅(-500)⋅(5)-n
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 10 Sequences and Series CCSS: HSF-BF.A.2
What is the explicit form of the sequence defined by a1=12;  an=12an-1, n>1?
  1. an=(12)n-1
  2. an=(12)⋅(12)-n
  3. an=(12)n
  4. an=12⋅(12)n
Grade 10 Sequences and Series CCSS: HSF-IF.A.3, HSF-BF.A.2, HSF-LE.A.2
Which formula represents the general term of the following sequence? 12,-1,2,-4,...
  1. an=12⋅2n
  2. an=12⋅(-2)⋅(n-1)
  3. an=12⋅-2n-1
  4. an=12⋅(-2)n-1
Grade 10 Sequences and Series CCSS: HSF-BF.A.1, HSF-BF.A.1a, HSF-LE.A.2
Given the sequence 1,-3,-9,-17,-27,..., which of the following functions correctly describes it? Assume that n∈ℕ.
  1. t(1)=1,t(2)=-3;  t(n)=t(n-1)-6t(n-2),n>2
  2. t(1)=1;  t(n)=t(n-1)-4, n>1
  3. t(1)=1;  t(n)=t(n-1)-2n, n>1
  4. t(1)=1;  t(n)=(-1)n-1⋅3⋅t(n-1),n>1
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.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
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.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
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