Arithmetic Sequences and Functions

This video tutorial explains arithmetic sequences and how they can be represented using explicit rules. It covers function notation, identifying arithmetic sequences, common mistakes, and deriving explicit rules. Examples are provided to illustrate finding specific terms in sequences, including those with negative common differences.

What is the function notation for a function where y is expressed in terms of x?

• y = x^2

• y = 2x - 3

• y = f(x)

• y = x + 2

In an arithmetic sequence, what is the term used to describe the number added or subtracted to get from one term to the next?

• Sequence factor

• Common ratio

• Arithmetic mean

• Common difference

Which of the following sequences is NOT arithmetic?

• 3, 6, 9, 13

• 7, 14, 21, 28

• 5, 10, 15, 20

• 2, 4, 6, 8

What is the explicit rule for an arithmetic sequence with a first term of 1 and a common difference of 3?

• a_n = 3n - 2

• a_n = 3n + 1

• a_n = n + 3

• a_n = 1 + 3(n - 1)

If the second term of an arithmetic sequence is 4, what is the common difference if the first term is 1?

• 2

• 3

• 4

• 5

How do you find the sixth term of an arithmetic sequence with the explicit rule a_n = 3n - 2?

• Multiply the first term by 6

• Add 3 to the fifth term

• Subtract 2 from the sixth term

• Substitute n = 6 into the rule

What is the explicit rule for a sequence with a first term of 18 and a common difference of -5?

• a_n = 18 + 5n

• a_n = 23 - 5n

• a_n = 23 + 5n

• a_n = 18 - 5n

What is the 12th term of the sequence with the explicit rule a_n = 23 - 5n?

• 23

• -23

• 37

• -37

In the sequence 18, 13, 8, ..., what is the common difference?

• -5

• 5

• 3

• -3

Which term number corresponds to the value -37 in the sequence with the rule a_n = 23 - 5n?

• 10

• 13

• 11

• 12