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In this lesson, we will learn how to represent arithmetic and geometric sequences as discrete functions and differentiate between finite and infinite sequences.

Q1:

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

Q2:

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

Q3:

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

Q4:

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

Q5:

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

Q6:

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

Q7:

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

Q8:

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

Q9:

Q10:

Q11:

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

Q12:

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

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

What is the number at position 12 341?

What is the range of this sequence?

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 .

Write a piecewise function that describes 𝑎 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.

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.

Describe the range of the function.

Q16:

Is each function whose domain is ℤ a sequence?

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.

Find the 27th term of the sequence.

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