16 Questions
What is the common ratio (R) of the geometric sequence 3, 12, 48, 192, ...?
4
Which of the following sequences is a geometric sequence?
3, 6, 18, 36, ...
What is the next term in the geometric sequence 2, 6, 18, ...?
54
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
What is the common ratio (R) of the geometric sequence 16, 8, 4, 2, ...?
2
Which of the following best describes the graph of a geometric sequence with a common ratio R > 1?
A curve that is concave up
Which type of growth is represented by a geometric sequence when R > 1?
Compound interest investments
If t0 = 3, what is the value of t1 using the given recurrence relation?
6
What does geometric decay represent?
Decreasing values by the same percentage
Which type of sequence involves reducing-balance depreciation?
Geometric decay
What is the common characteristic of geometric growth and decay?
Decreasing values at a constant rate
What is the recursive definition for the geometric sequence 2, 6, 18, ...
t_n+1 = 3t_n
Given the recursive definition t_0 = 5 and t_n+1 = 2t_n, what is the value of t_3?
40
Which of the following represents a geometric sequence?
1, 2, 4, 8, 16
If the first term of a geometric sequence is 3 and the common ratio is 2, what is the fourth term?
24
Which of the following sequences is an arithmetic sequence?
1, 3, 6, 10, 15
Test your understanding of geometric sequences by determining the common ratio, identifying geometric sequences, using CAS to generate a sequence, graphing sequences, and recognizing geometric growth and decay. Learn how each term in a geometric sequence is obtained by multiplying the previous term by a fixed ratio. Explore examples and applications of geometric sequences.
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