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Worksheet: Introduction to Sequences

In this worksheet, we will practice representing arithmetic and geometric sequences as discrete functions and differentiating between finite and infinite sequences.

Q1:

Is the sequence ( − 9 , − 6 , − 3 , 0 , … , 2 1 ) finite or infinite?

  • Afinite
  • Binfinite

Q2:

Is the sequence ( 1 4 , 1 7 , 2 0 , 2 3 , … ) finite or infinite?

  • Ainfinite
  • Bfinite

Q3:

Is the sequence ( − 8 8 , − 8 7 , − 8 6 , − 8 5 ) finite or infinite?

  • Afinite
  • Binfinite

Q4:

Is the sequence ( 7 2 , 7 7 , 8 2 , 8 7 , … , 1 2 2 ) finite or infinite?

  • Afinite
  • Binfinite

Q5:

Is the sequence with general term 3 𝑛 + 7 9 , where 𝑛 ∈ ℤ + , finite or infinite?

  • Ainfinite
  • Bfinite

Q6:

Is the sequence with general term 8 𝑛 − 2 2 3 , where 𝑛 ∈ ℤ + , finite or infinite?

  • Ainfinite
  • Bfinite

Q7:

Is the sequence with general term 5 𝑛 + 7 3 3 , where 𝑛 ∈ ℤ + , finite or infinite?

  • Ainfinite
  • Bfinite

Q8:

Find the range of the infinite arithmetic sequence represented in the figure below.

  • A
  • B
  • C
  • D
  • E

Q9:

Find the range of the infinite arithmetic sequence represented in the figure below.

  • A
  • B
  • C
  • D
  • E

Q10:

Find the range of the infinite arithmetic sequence represented in the figure below.

  • A
  • B
  • C
  • D
  • E

Q11:

If we consider a sequence to be a function, what is the function’s domain?

  • A ℝ +
  • B ℚ −
  • C ℤ −
  • D ℤ +
  • E ℝ −

Q12:

Consider the sequence given by 𝑓 ( 0 ) = 0 , 𝑓 ( 𝑛 + 1 ) = 1 − 𝑓 ( 𝑛 ) .

List the numbers at positions 2, 3, and 4.

  • A1, 1, 0
  • B1, 0, 1
  • C0, 0, 1
  • D0, 1, 0
  • E0, 1, 1

What is the number at position 12 341?

What is the range of this sequence?

  • A { 0 , 1 }
  • B { 1 , 2 }
  • C { 0 , 1 , 2 }
  • D { 2 , 3 , 4 }

Q13:

Consider the sequence − 1 , 2 , − 3 , 4 , − 5 , … .

Write the sequence of the first 5 odd terms: 𝑎 , 𝑎 , 𝑎 , 𝑎 , 𝑎 1 3 5 7 9 .

  • A − 2 , − 4 , − 6 , − 8 , − 1 0
  • B1, 3, 5, 7, 9
  • C2, 4, 6, 8, 10
  • D − 1 , − 3 , − 5 , − 7 , − 9
  • E − 1 , 2 , − 3 , 4 , − 5

Write a piecewise function that describes 𝑎 𝑛 .

  • A 𝑎 = − 𝑛 𝑛 𝑛 𝑛 𝑛 i f i s o d d i f i s e v e n
  • B 𝑎 = − 𝑛 𝑛 𝑛 + 1 𝑛 𝑛 i f i s o d d i f i s e v e n
  • C 𝑎 = 𝑛 𝑛 𝑛 − 1 𝑛 𝑛 i f i s o d d i f i s e v e n
  • D 𝑎 = 𝑛 + 1 𝑛 𝑛 𝑛 𝑛 i f i s o d d i f i s e v e n
  • E 𝑎 = 𝑛 − 1 𝑛 𝑛 + 1 𝑛 𝑛 i f i s o d d i f i s e v e n

Q14:

List the first 10 elements of the sequence where the 𝑛 th term is defined as the remainder when 𝑛 is divided by 4.

  • A 1 , 3 , 0 , 1 , 3 , 0 , 1 , 3 , 0 , 1 ,
  • B 1 , 2 , 0 , 1 , 2 , 0 , 1 , 2 , 0 , 1 ,
  • C 2 , 3 , 0 , 2 , 3 , 0 , 2 , 3 , 0 , 2 ,
  • D 1 , 2 , 3 , 0 , 1 , 2 , 3 , 0 , 1 , 2 ,
  • E 1 , 2 , 3 , 1 , 2 , 3 , 1 , 2 , 3 , 1 ,

What is the range of this sequence?

  • A { 0 , 1 , 2 , 3 }
  • B { 0 , 2 , 3 }
  • C { 0 , 1 , 3 }
  • D { 0 , 1 , 2 }
  • E { 1 , 2 , 3 }

Q15:

Consider the infinite sequence 4 , 7 , 1 0 , 1 3 , 1 6 , … . We can think of this sequence as a function whose graph is partially sketched.

Describe the domain of the function.

  • A ( 1 , ∞ )
  • BAll integers
  • C { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 }
  • DAll natural numbers: 1 , 2 , 3 , 4 , 5 , …
  • E { 0 , 1 , 2 , 3 , 4 , 5 , … }

Describe the range of the function.

  • AAll numbers 𝑦 satisfying 𝑦 = 3 𝑥 + 1 for integers 𝑥 ≥ 1
  • BAll numbers 𝑦 satisfying 𝑦 = 3 𝑥 + 1 for integers − ∞ < 𝑥 < ∞
  • CAll numbers 𝑦 satisfying 𝑦 = 3 𝑥 + 1 for integers 𝑥 ≥ 0
  • DAll numbers 𝑦 satisfying 𝑦 = 3 𝑥 + 1 for reals 𝑥 ≥ 1
  • EAll numbers 𝑦 satisfying 𝑦 = 3 𝑥 + 1 for integers 1 ≤ 𝑥 ≤ 8

Q16:

Is each function whose domain is ℤ a sequence?

  • Ano
  • Byes

Q17:

The graph of the first six terms of an arithmetic sequence is shown.

Write, in the form 𝑦 = 𝑚 𝑥 + 𝑏 , an equation for the sequence.

  • A 𝑦 = − 2 𝑥 − 5
  • B 𝑦 = 2 𝑥 + 5
  • C 𝑦 = 2 𝑥 − 5
  • D 𝑦 = − 2 𝑥 + 5
  • E 𝑦 = − 5 𝑥 + 8

Find the 27th term of the sequence.

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