Q 12.42 Determine if each sequence is ge... [FREE SOLUTION]

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Intermediate Algebra

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OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 12: Q 12.42 (page 1187)

Determine if each sequence is geometric. If so indicate the common ratio.
鈸� $鈭� 150, 鈭� 30, 鈭� 15, 鈭� 5, \frac{- 5}{2}, 0, 鈥�$
鈸� $5, 10, 20, 40, 80, 160, 鈥�$
鈸� $8, 4, 2, 1, \frac{1}{2}, \frac{1}{4}, 鈥�$

Short Answer

Expert verified

鈸� The sequence is not geometric.

鈸� The sequence is geometric with common ratio equal to 2

鈸� The sequence is geometric with common ratio equal to $\frac{1}{2}$

Step by step solution

Step 1. Given information

Sequences are given as follows:

鈸� $鈭� 150, 鈭� 30, 鈭� 15, 鈭� 5, \frac{- 5}{2}, 0, 鈥�$

鈸� $5, 10, 20, 40, 80, 160, 鈥�$

鈸� $8, 4, 2, 1, \frac{1}{2}, \frac{1}{4}, 鈥�$

Step 2. Determine if the sequence is geometric. If so indicate the common ratio.

Consider the sequence: $鈭� 150, 鈭� 30, 鈭� 15, 鈭� 5, \frac{- 5}{2}, 0, 鈥�$

A sequence is called a geometric sequence if the ratio between consecutive terms is always the same.

$\begin{array}{rcl} \frac{- 30}{- 150} & = & \frac{1}{5} \\ \frac{- 15}{- 30} & = & \frac{1}{2} \end{array}$

So,

$\begin{array}{rcl} \frac{- 30}{- 150} \end{array} 鈮� \begin{array}{rcl} \frac{- 15}{- 30} \end{array}$

Therefore, the sequence is not geometric.

Step 3. Determine if the sequence is geometric. If so indicate the common ratio.鈸� 5, 10, 20, 40, 80, 160, …

Consider the sequence: $5, 10, 20, 40, 80, 160, 鈥�$

role="math" localid="1645287422959" $\begin{array}{rcl} \frac{10}{5} & = & 2 \\ \frac{20}{10} & = & 2 \\ \frac{40}{20} & = & 2 \\ \frac{80}{40} & = & 2 \\ \frac{160}{80} & = & 2 \end{array}$

So,

$\begin{array}{rcl} \frac{10}{5} & = & \frac{20}{10} = \frac{40}{20} = \frac{80}{40} = \frac{160}{80} = 2 \end{array}$

So, the sequence is geometric with common ratio equal to $2$

Step 4. Determine if each sequence is geometric. If so indicate the common ratio.8, 4, 2, 1, 12 , 14 , …

Consider the sequence: $8, 4, 2, 1, \frac{1}{2}, \frac{1}{4}, 鈥�$

$\begin{array}{rcl} \frac{4}{8} & = & \frac{1}{2} \\ \frac{2}{4} & = & \frac{1}{2} \\ \frac{1}{2} & = & \frac{1}{2} \\ \frac{\frac{1}{2}}{1} & = & \frac{1}{2} \\ \frac{\frac{1}{4}}{\frac{1}{2}} & = & \frac{1}{2} \end{array}$

So,

$\frac{4}{8} = \frac{2}{4} = \frac{1}{2} = \frac{\frac{1}{2}}{1} = \frac{\frac{1}{4}}{\frac{1}{2}} = \frac{1}{2}$

Therefore, the series is geometric with common ratio equal to $\frac{1}{2}$

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91影视

Determine if each sequence is geometric. If so indicate the common ratio.
鈸� $鈭� 150, 鈭� 30, 鈭� 15, 鈭� 5, \frac{- 5}{2}, 0, 鈥�$
鈸� $5, 10, 20, 40, 80, 160, 鈥�$
鈸� $8, 4, 2, 1, \frac{1}{2}, \frac{1}{4}, 鈥�$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Determine if the sequence is geometric. If so indicate the common ratio.

Step 3. Determine if the sequence is geometric. If so indicate the common ratio.鈸� 5, 10, 20, 40, 80, 160, …

Step 4. Determine if each sequence is geometric. If so indicate the common ratio.8, 4, 2, 1, 12 , 14 , …

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91影视

Determine if each sequence is geometric. If so indicate the common ratio.鈸� 鈭�150,鈭�30,鈭�15,鈭�5,-52,0,鈥�鈸� 5,10,20,40,80,160,鈥�鈸�8,4,2,1,12,14,鈥�

Short Answer

Step by step solution

Step 1. Given information

Step 2. Determine if the sequence is geometric. If so indicate the common ratio.

Step 3. Determine if the sequence is geometric. If so indicate the common ratio.鈸� 5, 10, 20, 40, 80, 160, …

Step 4. Determine if each sequence is geometric. If so indicate the common ratio.8, 4, 2, 1, 12 , 14 , …

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Statistics

Logic and Functions

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Calculus

Study anywhere. Anytime. Across all devices.

Determine if each sequence is geometric. If so indicate the common ratio.
鈸� $鈭� 150, 鈭� 30, 鈭� 15, 鈭� 5, \frac{- 5}{2}, 0, 鈥�$
鈸� $5, 10, 20, 40, 80, 160, 鈥�$
鈸� $8, 4, 2, 1, \frac{1}{2}, \frac{1}{4}, 鈥�$