Identifying Geometric Sequences and Recursive Formulas

The video tutorial introduces geometric sequences, explaining how to identify them through graphing and recognizing patterns. It discusses the concept of a common ratio and how it is used to determine if a sequence is geometric. The tutorial also covers finding the next terms in a sequence using the common ratio and explains recursive formulas in both subscript and function notation.

What operation remains constant in a geometric sequence?

• Multiplication

• Subtraction

• Addition

• Division

What is the common ratio if a sequence progresses from 2 to 6?

• 2

• 3

• 4

• 5

Is the sequence 1, 2, 4, 7 geometric?

• None of the above

• Yes

• No

• Cannot be determined

What is the common ratio for a sequence decreasing from 512 to 128?

• 1/5

• 1/4

• 1/3

• 1/2

What is the next term in the sequence after 20, if the common ratio is 1/5?

• 10

• 4

• 15

• 5

What is the common ratio if the sequence terms are negative and the sequence is not oscillating?

• 2

• -3

• 3

• -2

If the recursive formula is 'a n = 3 * a (n-1)', what is the third term if the first term is 7?

• 21

• 42

• 63

• 84

What does subscript notation in a recursive formula indicate?

• The sequence length

• The term number

• The common ratio

• The sequence sum

In function notation, what does 'f of n' represent?

• The product of the first n terms

• The difference between terms

• The sum of the first n terms

• The nth term of the sequence

What is the first term of a sequence if a1 is defined as 640 in subscript notation?

• 160

• 10

• 640

• 40