Exploring Arithmetic and Geometric Sequences

The video tutorial explains sequences, focusing on arithmetic and geometric types. Arithmetic sequences involve adding a constant number, while geometric sequences involve multiplying by a constant factor. The tutorial provides rules to identify each type and offers examples for practice. It emphasizes understanding the pattern of change in sequences to determine their type.

What defines a sequence?

• A list of numbers without any specific order

• A series of numbers following a fixed pattern

• A collection of numbers randomly arranged

• A group of numbers sorted in ascending order

What operation is used in arithmetic sequences?

• Division

• Multiplication

• Subtraction

• Addition

What is the common difference in the sequence 2, 4, 6, 8?

• 3

• 4

• 2

• 1

What indicates a sequence is decreasing in an arithmetic sequence?

• A positive common difference

• A negative common difference

• A negative common ratio

• A positive common ratio

How is a geometric sequence identified?

• By the subtraction of a constant number

• By the addition of a constant number

• By the multiplication by a constant factor

• By the division by a constant number

In a geometric sequence, if the first term is 5 and the common ratio is 3, what is the third term?

• 135

• 45

• 405

• 15

Which sequence is an example of a geometric sequence?

• 2, 4, 6, 8

• 1, 2, 3, 4

• 3, 6, 12, 24

• 5, 10, 15, 20

What is the next number in the arithmetic sequence 4, 9, 14?

• 21

• 19

• 20

• 18

If a sequence is neither arithmetic nor geometric, what could be the reason?

• The sequence increases by a fixed factor

• The sequence does not increase or decrease by a fixed number or factor

• The sequence decreases by the same number

• The sequence increases by the same number

For the sequence 1, 3, 9, 27, what is the common ratio?

• 4

• 3

• 2

• 5