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Sequences and Series Questions - All Grades

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Grade 9 Sequences and Series CCSS: HSF-BF.A.2
For the sequence defined by the explicit formula an=7+3n, what is the the recursive formula for this sequence?
  1. a1=7;  an=an-1+3, n>1
  2. a1=10;  an=an-1+3, n>1
  3. a1=3;  an=an-1+7, n>1
  4. a1=1;  an=an-1+7, n>1
Grade 9 Sequences and Series
What type of sequence is the following? 8,5,2,-1,...
  1. Arithmetic
  2. Geometric
  3. Neither
Grade 10 Sequences and Series CCSS: HSF-IF.A.3, HSF-BF.A.2, HSF-LE.A.2
What is the recursive function of the geometric sequence 3, 4.5, 6.75...?
  1. f(n)=1.5f(n-1) where f(1)=3
  2. f(n)=3×1.5n-1
  3. f(n)=1.5×3n-1
  4. f(n)=3f(n-1) where f(1)=1.5
Grade 10 Sequences and Series CCSS: HSF-IF.A.3
Match the function to its corresponding sequence:
__ a(x)=5(x+3)2 A. 80,125,180,245,320...
__ a(x)=x2-x B. 18,24,42,96,258...
__ a(x)=2x2+3x3 C. 5,32,99,224,425...
__ a(x)=3x+15 D. 0,2,6,12,20...
Grade 11 Sequences and Series CCSS: HSF-IF.A.3
In an arithmetic sequence, if the 4th term is 3 and the 22nd term is 15, then what is the 1st term?
  1. 23
  2. 1
  3. -3
  4. -43
  5. none of these are correct
Grade 11 Sequences and Series CCSS: HSA-SSE.B.4

This question is a part of a group with common instructions. View group »

How does one go from step 3 to step 4?
  1. Use polynomial long division.
  2. Apply the fundamental theorem of algebra.
  3. Factor out common factors on both sides.
  4. Multiply each side by (1-r).
Grade 10 Sequences and Series CCSS: HSF-IF.A.3
Determine d for the following sequence: 4,7,10,13,16....
  1. 3
  2. 4
  3. 16
  4. 1
  5. none of these are correct
Grade 11 Sequences and Series CCSS: HSA-SSE.B.4
What is the approximate sum of the first 16 numbers in the series 19+127+181+...?
  1. 0.000167
  2. 5.4×10-16
  3. 1.67
  4. 0.167
Grade 9 Sequences and Series CCSS: HSF-IF.A.3
Find the next three terms for the sequence. 14,34,54,74,94,...
  1. 114, 134, 154
  2. 188, 208, 228
  3. 104, 124, 144
  4. 84, 104, 124
Grade 9 Sequences and Series CCSS: HSF-BF.A.2
For the sequence defined by a1=4;  an=an-1-4,n>1, which of the following describes the same sequence? There may be more than one correct answer.
  1. an=8-4n
  2. an=4-4(n-1)
  3. an=4-4n
  4. an=-4-4(n-3)
Grade 9 Sequences and Series CCSS: HSF-BF.A.2
What is the recursive form of the sequence an=16-20n?
  1. a1=-20;  an=an-1+16, n>1
  2. a1=16;  an=an-1-20, n>1
  3. a1=-4;  an=an-1+16, n>1
  4. a1=-4;  an=an-1-20, n>1
Grade 9 Sequences and Series CCSS: HSF-BF.A.2
Find the explicit formula of the sequence defined by a1=85;  an=an-1-15, n>1.
  1. an=85-15n
  2. an=-15+100n
  3. an=100-15n
  4. an=85-100n
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 10 Sequences and Series CCSS: HSF-IF.A.3
Determine the 20th term for the following sequence: 1,8,15,22,29...
  1. 79
  2. 325
  3. 57
  4. 215
  5. none of these are correct
Grade 11 Sequences and Series CCSS: HSA-SSE.B.4
What is the sum of the first 12 numbers in the series 8+24+72+216+648+...?
  1. 2,125,760
  2. 6.87×1010
  3. 531,441
  4. -2,125,760
Grade 11 Sequences and Series CCSS: HSA-SSE.B.4

This question is a part of a group with common instructions. View group »

Where does the equation in step one come from?
  1. From the definition of a geometric series.
  2. From a well known polynomial identity.
  3. It is an assumption.
  4. It is simply a new and arbitrary definition of Sn.
Grade 9 Sequences and Series
What type of sequence is this: 2, -4, 8, -16,...?
  1. Arithmetic
  2. Geometric
  3. Neither
Grade 10 Sequences and Series CCSS: HSF-IF.A.3
Match the function to its corresponding sequence:
__ f(n)=6+3n2 A. 3,9,25,65,161...
__ f(n)=n3-5 B. 9,18,33,54,81...
__ f(n)=12n+7 C. 7.5,8,8.5,9,9.5...
__ f(n)=(2x)⋅x+1 D. -4,3,22,59,120...
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