Sequence Lesson

Multiple Choice

Which of the following best describes a sequence?

• A random collection of numbers

• An ordered list of elements

• A single number repeated

• A group of unrelated objects

Multiple Choice

Which of the following best describes the pattern in the number of squares in each term of the sequence shown in the first image?

• Each term doubles the number of squares from the previous term.

• Each term adds 2 squares to the previous term.

• Each term subtracts 2 squares from the previous term.

• Each term triples the number of squares from the previous term.

Fill in the Blank

The fixed amount that is being added or subtracted in an arithmetic sequence is known as the ___ difference.

Multiple Choice

Which of the following sequences is an arithmetic sequence?

• 2, 4, 8, 16, ...

• 5, 10, 15, 20, ...

• 3, 6, 12, 24, ...

• 10, 5, 2.5, 1.25, ...

Multiple Choice

Given the sequence 1, 6, 11, 16, 21, ..., what is the value of the 7th term?

• 26

• 31

• 36

• 41

Multiple Choice

Which sequence below has a common difference of 3?

• (1)

• (2)

• (3)

• (4)

Multiple Choice

What is the common difference of a sequence with a 1st term of 6 and the 4th term of 18?

• 2

• 3

• 4

• 6

Open Ended

Explain how the common difference in an arithmetic sequence can be interpreted as the slope. Provide an example using the sequence from the image.

Fill in the Blank

Fill in the blank: The domain of the function for an arithmetic sequence is the set of positive ___ .

Multiple Choice

Which of the following statements about subscript notation in sequences is correct?

• The subscript represents the value of the term.

• The subscript represents the position of the term in the sequence.

• The subscript is always equal to the term value.

• The subscript is used only for odd terms.

Multiple Select

Select all correct statements about the arithmetic sequence a(n) where a(1) = 5 and d = 3.

• The first term is 5.

• The common difference is 3.

• The sequence decreases by 3 each time.

• The fifth term is 17.

Multiple Choice

What is the recursive formula for the arithmetic sequence where a(1) = 5 and the common difference d = 3?

• a(n+1) = a(n) + 3

• a(n+1) = a(n) - 3

• a(n+1) = a(n) + 5

• a(n+1) = a(n) + n

Multiple Choice

Which of the following statements correctly describes how to find the next term in the sequence defined by f(1) = 3 and f(n) = f(n-1) + 9?

• Add 9 to the previous term

• Subtract 9 from the previous term

• Multiply the previous term by 9

• Divide the previous term by 9

Fill in the Blank

Fill in the blank: The first term of the sequence defined by f(1) = 17 and f(n+1) = f(n) - 4 is ___.

Multiple Select

Select all sequences that have a common difference of 7.

• 6, 13, 20, 27, ...

• 20, 27, 34, 41, ...

• 2, 9, 16, 23, ...

• 1, 8, 15, 22, ...

Multiple Choice

In a sequence, the first term is 4 and the common difference is 3. What is the fifth term of this sequence?

• -11

• -8

• 16

• 19

Multiple Choice

Which recursively defined function has a first term equal to 10 and a common difference of 4?

• f(1) = 10, f(x) = f(x-1) + 4

• f(1) = 4, f(x) = f(x-1) + 10

• f(1) = 10, f(x) = 4f(x-1)

• f(1) = 4, f(x) = 10f(x-1)

Open Ended

Explain how the tables in the image demonstrate that both functions are linear. What feature of the tables supports this conclusion?

Multiple Choice

How many times would you add the common difference to reach the 20th term in the arithmetic sequence shown?

• 9 times

• 10 times

• 19 times

• 20 times

Fill in the Blank

What is the common difference in the arithmetic sequence shown, and how is it used to find the 10th term?

Open Ended

Why is it helpful to think of arithmetic sequences in the same way as linear functions?

Multiple Choice

Which part of the equation y - y₁ = m(x - x₁) represents the common difference in an arithmetic sequence?

• m

• x₁

• y₁

• x

Multiple Choice

How many shaded squares will there be in the 4th term of the sequence?

• 20

• 22

• 24

• 28

Open Ended

What is a sequence in mathematics, and how are the terms of a sequence defined?