Geometric Sequences and Common Ratio Quiz

Play an AI-generated podcast conversation about this lesson

What is the common ratio (R) of the geometric sequence 3, 12, 48, 192, ...?

6

12

3

4 (correct)

Which of the following sequences is a geometric sequence?

3, 6, 18, 36, ... (correct)

1, 3, 5, 7, ...

5, 10, 15, 20, ...

2, 10, 50, 250, ...

What is the next term in the geometric sequence 2, 6, 18, ...?

24

54 (correct)

36

72

What is the term number (n) and term value (t_n) for the fourth term in the geometric sequence 2, 6, 18, ...?

n = 4, t_n = 54 Signup and view all the answers

What is the common ratio (R) of the geometric sequence 16, 8, 4, 2, ...?

2 Signup and view all the answers

Which of the following best describes the graph of a geometric sequence with a common ratio R > 1?

A curve that is concave up Signup and view all the answers

Which type of growth is represented by a geometric sequence when R > 1?

Compound interest investments Signup and view all the answers

If t0 = 3, what is the value of t1 using the given recurrence relation?

6 Signup and view all the answers

What does geometric decay represent?

Decreasing values by the same percentage Signup and view all the answers

Which type of sequence involves reducing-balance depreciation?

Geometric decay Signup and view all the answers

What is the common characteristic of geometric growth and decay?

Decreasing values at a constant rate Signup and view all the answers

What is the recursive definition for the geometric sequence 2, 6, 18, ...

t_n+1 = 3t_n Signup and view all the answers

Given the recursive definition t_0 = 5 and t_n+1 = 2t_n, what is the value of t_3?

40 Signup and view all the answers

Which of the following represents a geometric sequence?

1, 2, 4, 8, 16 Signup and view all the answers

If the first term of a geometric sequence is 3 and the common ratio is 2, what is the fourth term?

24 Signup and view all the answers

Which of the following sequences is an arithmetic sequence?

1, 3, 6, 10, 15 Signup and view all the answers

Geometric Sequences and Common Ratio Quiz

Podcast Beta

Questions and Answers