Exploring Arithmetic Sequences

The video tutorial explains arithmetic sequences, highlighting their similarity to linear equations. It covers the concept of a common difference and how to derive the sequence equation. An example sequence is analyzed, and the process of finding specific terms, such as the 100th term, is demonstrated. The tutorial also shows how to determine if a given value is part of the sequence, emphasizing the need for whole number terms.

What is an arithmetic sequence?

• A sequence where each term is multiplied by a common ratio.

• A sequence where each term is a cube of the previous term.

• A sequence where each term is a square of the previous term.

• A sequence where each term is added or subtracted by a common difference.

In the equation y = mx + b, what does 'm' represent?

• The y-intercept

• The term number

• The x-intercept

• The slope or rate of change

In arithmetic sequences, what does 'n' represent?

• The term number

• The y-intercept

• The term value

• The common difference

What is the common difference in the sequence 4, 7, 10, 13?

• 5

• 4

• 3

• 2

What are the next three terms in the sequence 4, 7, 10, 13?

• 17, 20, 23

• 18, 21, 24

• 15, 18, 21

• 16, 19, 22

How do you find the zero term of an arithmetic sequence?

• By adding the common difference to the first term

• By subtracting the common difference from the first term

• By multiplying the first term by the common difference

• By dividing the first term by the common difference

What is the zero term of the sequence 4, 7, 10, 13?

• 2

• 1

• 3

• 0

What is the equation of the sequence with a common difference of 3 and a zero term of 1?

• T(n) = n - 3

• T(n) = 3n - 1

• T(n) = 3n + 1

• T(n) = n + 3

What is the 100th term of the sequence with the equation T(n) = 3n + 1?

• 300

• 299

• 301

• 298

Is 126 a term in the sequence with the equation T(n) = 3n + 1?

• No, it is not a term

• Yes, it is the 43rd term

• Yes, it is the 41st term

• Yes, it is the 42nd term