Identifying Arithmetic Sequences and Recursive Formulas

The video tutorial introduces arithmetic sequences, explaining their properties and how to identify them by finding the common difference. It covers the concept of recursive formulas, demonstrating how to write them in both subscript and function notation. The tutorial includes examples and exercises to practice identifying sequences and writing recursive formulas.

What is an arithmetic sequence?

• A sequence with random differences between terms

• A sequence with varying differences between terms

• A sequence where each term decreases by a fixed number

• A sequence where each term increases by a fixed number

If a sequence starts with 1, 4, 7, what is the common difference?

• 2

• 3

• 4

• 5

Which sequence is not an arithmetic sequence?

• 10, 13, 17, 21

• 2, 5, 8, 11

• 3, 3, 3, 3

• 5, 10, 15, 20

What is the common difference in the sequence 7, 7, 7, 7?

• -1

• 0

• 1

• 7

What are the next three terms of the sequence 2, 6, 10?

• 14, 18, 22

• 12, 14, 16

• 15, 20, 25

• 13, 16, 19

What does a recursive formula provide in a sequence?

• The next term based on the sum of all previous terms

• The next term based on the difference from the previous term

• The next term based on the product of the previous terms

• The next term based only on the first term

How do you find the first term in a sequence using function notation?

• f(0)

• f(1)

• f(a)

• f(n)

What is the common difference in the sequence defined by the recursive formula a(n) = a(n-1) + 5?

• 10

• 5

• -5

• 0

If the first term of a sequence is 10 and the common difference is -2, what is the third term?

• 16

• 14

• 8

• 6

In function notation, how is the third term represented?

• f(3)

• f(2)

• f(1)

• f(n)