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Sequences and Series Questions - All Grades

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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 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 10 Sequences and Series CCSS: HSF-IF.A.3
What are the fifth and seventh numbers in the sequence 1,6,36...?
  1. 216,7776
  2. 216,1296
  3. 7776,46656
  4. 1296,46656
Grade 9 Sequences and Series CCSS: HSF-IF.A.3
In the following sequence, what is the common difference? -2, 1, 4, 7, ...
  1. -2
  2. 3
  3. 7
  4. None of the above
Grade 10 Sequences and Series CCSS: HSF-IF.A.3
A given arithmetic sequence is described by the function f(1)=-8;  f(n)=f(n-1)+4,n≥2. Does the function f(1)=-8;f(n)=f(n-2)+8,n≥3 describe the same sequence? If not, why?
  1. Yes, these are the same sequences.
  2. No, the second sequence doesn't define its second term, and therefore isn't complete.
  3. No, they have different recursive relationships.
  4. No, they have different domains.
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 10 Sequences and Series CCSS: HSF-BF.A.2
For the geometric sequence defined by a1=80;  an=12an-1,n>1, what is the explicit form of this sequence?
  1. an=80(12)n
  2. an=80(12)n-1
  3. an=80⋅2n-1
  4. a1=1⋅(12)n
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 9 Sequences and Series CCSS: HSF-IF.A.3
What is the common difference in the following sequence? 13, 15, 17, 19, ...
  1. d = 1
  2. d = -2
  3. d = 2
  4. d = 0
Grade 11 Sequences and Series
Find the 17th term of this sequence. an=(-1)n-1⋅n2
  1. -289
  2. 265
  3. 289
  4. -256
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 11 Sequences and Series CCSS: HSF-IF.A.3, HSF-BF.A.2, HSF-LE.A.2
What is tn for the sequence 14/3, 16/3, 6, 20/3, 22/3, ...?
  1. tn=23n+113
  2. tn=23n+4
  3. tn=23n+123
  4. tn=23n+6
Grade 9 Sequences and Series CCSS: HSF-IF.A.3
What is the seventh term of the sequence 24, 12, 6, 3,...?
  1. 0
  2. 0.25
  3. 0.375
  4. 1.5
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