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Chapter 3: Q17. (page 108)

For each exercise, write the equation you think should come next. Check your prediction with a calculator.

92=81992=98019992=998001

Short Answer

Expert verified

The next equation must be 99992=99980001.

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 sequence

92=81992=98019992=998001

reason inductively that is., we can conclude based on past observations

As,

9鈫�99鈫�99981鈫�9801鈫�998001

raised to the power square is fixed.

03

Step 3. Predict the next equation.

So, as per the pattern of the sequence, next terms in the equation will be:

9鈫�99鈫�999鈫�9999炉81鈫�9801鈫�998001鈫�99980001炉

Therefore, the next equation must be 99992=99980001.

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