Q15. 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: Q15. (page 110)

Use inductive reasoning to predict the next number in each sequence.
1,4,2,8,4,16,8,32,...

Short Answer

Expert verified

Sequence with next number is $1, 鈥夆赌� 4, 鈥夆赌� 2, 鈥夆赌� 8, 鈥夆赌� 4, 鈥夆赌� 16, 鈥夆赌� 8, 鈥夆赌� 32, 鈥夆赌� \underset{炉}{16} ...$ .

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 1,4,2,8,4,16,8,32,... reason inductively that is., we can conclude based on past observations

As,

$a_{1} = 1 a_{2} = 4 a_{3} = 2 a_{1} = 2 a_{4} = 2 a_{2} = 8 a_{5} = 2 a_{3} = 4 a_{6} = 2 a_{4} = 16 a_{7} = 2 a_{5} = 8 a_{8} = 2 a_{6} = 32$

So, the pattern of the sequence is that two alternate sequences are there {1,2,4,8鈥 and {4,8,16,32}, wherein each term is getting multiplied by 2 to obtain next term.

Step 3. Predict the next number of the sequence.

Since, the pattern of the sequence is that two alternate sequences are there {1,2,4,8鈥 and {4,8,16,32}, wherein each term is getting multiplied by 2 to obtain next term., therefore, the next term of the sequence will be,

$a_{9} = 2 a_{7} = 16$ .

Therefore, the sequence will be $1, 鈥夆赌� 4, 鈥夆赌� 2, 鈥夆赌� 8, 鈥夆赌� 4, 鈥夆赌� 16, 鈥夆赌� 8, 鈥夆赌� 32, 鈥夆赌� \underset{炉}{16} ...$ .