Arithmetic Sequences and Their Properties

The video tutorial covers arithmetic sequences, starting with definitions and examples of finite and infinite sequences. It explains how to find unknown terms, calculate the number of terms, and determine the common difference using arithmetic sequence formulas. The tutorial includes four problem-solving examples to illustrate these concepts.

What is a sequence?

• A function with a finite or infinite domain

• A set of numbers with no specific order

• A set of random numbers

• A function with only a finite domain

In an arithmetic sequence, how is each term after the first obtained?

• By dividing by a constant

• By subtracting a constant

• By adding a constant

• By multiplying a constant

What is the common difference in the sequence 3, 6, 9, 12, 15?

• 2

• 3

• 5

• 4

Given the sequence 5, __, 13, 17, what is the second term?

• 9

• 7

• 10

• 8

What is the common difference in the sequence 5, __, 13, 17?

• 5

• 2

• 3

• 4

What is the formula for finding the nth term in an arithmetic sequence?

• a_n = a_1 - (n - 1) * d

• a_n = a_1 * (n - 1) + d

• a_n = a_1 / (n - 1) + d

• a_n = a_1 + (n - 1) * d

If the first term is 2 and the common difference is 2, what is the 45th term?

• 90

• 94

• 88

• 92

How many terms are in the arithmetic sequence with the first term 9, common difference 7, and last term 212?

• 30

• 31

• 29

• 28

What is the position of the last term in the sequence with the first term 9, common difference 7, and last term 212?

• 28

• 31

• 29

• 30

Given the first term 21 and the 30th term 427, what is the common difference?

• 12

• 13

• 14

• 15