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Chapter 3: Q8WE. (page 107)

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

8,  −4,  2,  −1,  12,....

Short Answer

Expert verified

Sequence with next two numbers is 8, −4, 2,−1, 12,  −14¯, 18¯,....

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.

While looking for a pattern in the sequence8, −4, 2,−1, 12,  .... reason inductively that is., we can conclude based on past observations.

Observe that,

8×−12=−4−4×−12=22×−12=−1−1×−12=12

So, the pattern of the sequence is that the next term is−12 times the previous term.

03

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

So, the next two term of the sequence will be12×−12=−14and −14×−12=18.

Therefore, the sequence will be, 8, −4, 2,−1, 12,  −14¯, 18¯,....

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Most popular questions from this chapter

Exercises 23 – 29 refer to the diagram in Step 2 of Exercise 22

How many pairs of parallel planes are shown?

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