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Chapter 3: Q4WE. (page 107)

Look for a pattern and predict the next two numbers in each sequence.

1,  4,  9,  16,  ....

Short Answer

Expert verified

Sequence with next two numbers is 1, 4, 9, 16, 25¯, 36¯, ....

Step by step solution

01

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.

02

Step 2. Look for a pattern.

Here the given sequence can be written as,

1, 4, 9, 16, ....≈12, 22, 32, 42, ....

Therefore, while looking for a pattern we can reason inductively that is., we can conclude based on past observations. So, the following numbers are the sequence of numbers.

03

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

Since the sequence is squares of natural numbers, so, the next two terms of the sequence according to the pattern is 52 and62which is equal to 25 and 36.

So, the sequence will be, 1, 4, 16, 64, 25¯, 36¯, ....

Therefore, the sequence with the next two numbers is 1, 4, 16, 64, 25¯, 36¯, .....

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