Q21. Use inductive reasoning to predi... [FREE SOLUTION]

91影视

Geometry

Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 227 pages

ISBN: 9780395977279

Chapter 3: Q21. (page 112)

Use inductive reasoning to predict the next two numbers in each sequence.
$100, 鈥夆赌� 鈭� 10, 鈥夆赌� 1, 鈥夆赌� 鈭� \frac{1}{10}, 鈥夆赌� ....$ .

Short Answer

Expert verified

Sequence with next two numbers is ~~$100, 鈥夆赌� 鈭� 10, 鈥夆赌� 1, 鈥夆赌� 鈭� \frac{1}{10}, 鈥夆赌� \underset{炉}{\frac{1}{100}}, 鈥� \underset{炉}{鈭� \frac{1}{1000}}, ...$~~ .

Step by step solution

Step 1. Define inductive reasoning.

Inductive reasoning is conclusions based on several past observations.

Step 2. Look for a pattern.

While looking for a pattern in the sequence $100, 鈥夆赌� 鈭� 10, 鈥夆赌� 1, 鈥夆赌� 鈭� \frac{1}{10}, 鈥夆赌� ...$ reason inductively that is., we can conclude based on past observations.

Observe that,

$\begin{matrix} 100 脳 (鈭� \frac{1}{10}) = 鈭� 10 \\ 鈭� 10 脳 (鈭� \frac{1}{10}) = 1 \\ 1 脳 (鈭� \frac{1}{10}) = 鈭� \frac{1}{10} \end{matrix}$

So, the pattern of the sequence is that the next term is $(鈭� \frac{1}{10})$ times the previous term.

Step 3. Predict the next two numbers of the sequence.

So, the next two term of the sequence will be $鈭� \frac{1}{10} 脳 (鈭� \frac{1}{10}) = \frac{1}{100}$ and $\frac{1}{100} 脳 (鈭� \frac{1}{10}) = 鈭� \frac{1}{1000}$ .

Therefore, the sequence will be, $100, 鈥夆赌� 鈭� 10, 鈥夆赌� 1, 鈥夆赌� 鈭� \frac{1}{10}, 鈥夆赌� \underset{炉}{\frac{1}{100}}, 鈥� \underset{炉}{鈭� \frac{1}{1000}}, ...$ .

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91影视

Use inductive reasoning to predict the next two numbers in each sequence.
$100, 鈥夆赌� 鈭� 10, 鈥夆赌� 1, 鈥夆赌� 鈭� \frac{1}{10}, 鈥夆赌� ....$ .

Short Answer

Step by step solution

Step 1. Define inductive reasoning.

Step 2. Look for a pattern.

Step 3. Predict the next two numbers of the sequence.

One App. One Place for Learning.

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91影视

Use inductive reasoning to predict the next two numbers in each sequence.100,鈥夆赌�鈭�10,鈥夆赌�1,鈥夆赌�鈭�110,鈥夆赌�.....

Short Answer

Step by step solution

Step 1. Define inductive reasoning.

Step 2. Look for a pattern.

Step 3. Predict the next two numbers of the sequence.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Statistics

Geometry

Pure Maths

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Calculus

Study anywhere. Anytime. Across all devices.

Use inductive reasoning to predict the next two numbers in each sequence.
$100, 鈥夆赌� 鈭� 10, 鈥夆赌� 1, 鈥夆赌� 鈭� \frac{1}{10}, 鈥夆赌� ....$ .