Q8 Look for a pattern and predict t... [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: Q8 (page 107)

Look for a pattern and predict the next two numbers in each sequence.
$8, 鈥夆赌� 鈭� 4, 鈥夆赌� 2, 鈥夆赌� 鈭� 1, 鈥夆赌� \frac{1}{2}, ....$

Short Answer

Expert verified

Sequence with next two numbers is $8, 鈥� 鈭� 4, 鈥� 2, 鈭� 1, 鈥� \frac{1}{2}, 鈥夆赌� \underset{炉}{鈭� \frac{1}{4}}, 鈥� \underset{炉}{\frac{1}{8}}, . ..$ .

Step by step solution

Step 1. Define deductive and inductive reasoning

Deductive reasoning is conclusions based on accepted statements like a theorem, postulate, facts etc.

Inductive reasoning is conclusions based on several past observations.

Step 2. Look for a pattern

While looking for a pattern in the sequence $8, 鈥� 鈭� 4, 鈥� 2, 鈭� 1, 鈥� \frac{1}{2}, 鈥夆赌� ....$ reason inductively that is., we can conclude based on past observations.

$\begin{matrix} 8 脳 (鈭� \frac{1}{2}) = 鈭� 4 \\ 鈭� 4 脳 (鈭� \frac{1}{2}) = 2 \\ 2 脳 (鈭� \frac{1}{2}) = 鈭� 1 \\ 鈭� 1 脳 (鈭� \frac{1}{2}) = \frac{1}{2} \end{matrix}$

Observe that,

So, the pattern of the sequence is that the next term is $(鈭� \frac{1}{2})$ times the previous term.

Step 3. Predict the next two numbers of the sequence

So, the next two term of the sequence will be $\frac{1}{2} 脳 (鈭� \frac{1}{2}) = 鈭� \frac{1}{4}$ and $鈭� \frac{1}{4} 脳 (鈭� \frac{1}{2}) = \frac{1}{8}$ .