Exploring Arithmetic Sequences and Finding Explicit Rules

This video tutorial explains arithmetic sequences and how they can be represented using an explicit rule. It covers the concept of common differences, demonstrates how to derive the explicit rule, and applies it to find specific terms in a sequence. The tutorial also highlights common mistakes when identifying arithmetic sequences and provides examples to clarify these concepts.

What is the function notation for a relation where y is the output and x is the input?

• y = f(x)

• y = 2x - 3

• y = x^2

• y = x + 2

In an arithmetic sequence, what must be true about the difference between consecutive terms?

• It must increase by 1 each time.

• It must be a positive number.

• It must be a negative number.

• It must be the same for each pair of terms.

Which of the following sequences is NOT arithmetic?

• 2, 4, 6, 8

• 5, 10, 15, 20

• 3, 6, 9, 13

• 7, 14, 21, 28

What is the general form of the explicit rule for an arithmetic sequence?

• a_n = a_1 - d(n - 1)

• a_n = a_1 + d(n - 1)

• a_n = a_1 + d(n + 1)

• a_n = a_1 * d(n - 1)

If the first term of an arithmetic sequence is 1 and the common difference is 3, what is the explicit rule?

• a_n = 3n + 2

• a_n = 3n - 1

• a_n = 3n - 2

• a_n = 3n + 1

Using the explicit rule a_n = 3n - 2, what is the 6th term of the sequence?

• 15

• 16

• 14

• 17

For the sequence with the explicit rule a_n = 23 - 5n, what is the 12th term?

• -40

• -35

• -37

• -39