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Sequences and Series Questions - All Grades

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Grade 10 Sequences and Series CCSS: HSF-BF.A.2
Given the recursive form of the sequence a1=27;  an=3an-1, n>1, find the correct explicit form of this sequence.
  1. an=221⋅3n
  2. an=27⋅3n
  3. an=27⋅3n
  4. an=(67)n-1
Grade 11 Sequences and Series CCSS: HSA-SSE.B.4

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The equation in the third step is found by subtracting the equation from step 2 from the equation in step 1. What happens to all the terms on the right hand side?
  1. They are ignored, because they are all going to be much smaller than either a or arn, depending on whether r is greater or less than 1.
  2. All but two of them are eliminated by subtraction. Aside from the first term of the first equation and the last term of the second equation, each term in the first equation has an equal term in the second equation, and thus they become n - 2 zeros.
  3. Using the factor theorem, they all cancel out except for a and arn.
  4. Dividing both sides of the equation by ar,ar2,...,arn-1, they all cancel out.
Grade 11 Sequences and Series CCSS: HSA-SSE.B.4

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How does one arrive at step 2?
  1. It is a new definition for Sn.
  2. Adding a factor of r to each term.
  3. By multiplying each side of the equation in step one by r.
  4. Adding a similar, but larger, finite geometric series.
Grade 10 Sequences and Series CCSS: HSF-BF.A.1, HSF-BF.A.1a, HSF-LE.A.2
Which of the following functions correctly describes the sequence 1,3,5,9,13,21,...? Assume that n∈ℕ.
  1. t(1)=1,t(2)=3;  t(n)=2t(n-2)+3,n>2
  2. t(1)=1;  t(n)=t(n-1)+2,n>1
  3. t(1)=1,t(2)=3;  t(n)=t(n-2)+t(n-1)+1,n>2
  4. t(1)=1;  t(n)=t(n-1)+2n-1, n>1
Grade 10 Sequences and Series CCSS: HSF-IF.A.3
Which of the following functions express the sequence -12,-9,-6,-3,0...?
  1. f(x)=12x+10
  2. f(x)=-9x2
  3. f(x)=3x-15
  4. f(x)=45x-3
Grade 10 Sequences and Series
Determine the fourth term of the sequence defined by a1=20 and an=an-1n2.
  1. 80
  2. 20
  3. 5
  4. 1
  5. none of these are correct
Grade 11 Sequences and Series
Find the 12th term of this sequence. an=(-1)n+1⋅en2
  1. -144
  2. 144
  3. -e144
  4. e144
Grade 10 Sequences and Series CCSS: HSF-BF.A.2
What is the recursive form of the sequence defined by a1=2;  an=5an-1, n>1?
  1. an=2⋅5n
  2. an=2⋅5n+1
  3. an=(25)⋅5n
  4. an=(25)⋅5n-1
Grade 11 Sequences and Series CCSS: HSA-SSE.B.4

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

Are there any restrictions one should have added at the beginning of this derivation? Choose all that apply.
  1. No, this correct as is.
  2. Yes, this derivation is only valid for a>0.
  3. Yes, the formula found is only true if |r|<1.
  4. Yes, it must be stated that r≠1.
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