Chapter 3: Q21. (page 112)

Use inductive reasoning to predict the next two numbers in each sequence.
$100, - 10, 1, - \frac{1}{10}, ....$ .

Short Answer

Expert verified

Sequence with next two numbers is ~~$100, - 10, 1, - \frac{1}{10}, \underline{\frac{1}{100}}, \underline{- \frac{1}{1000}}, ...$~~ .

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 $100, - 10, 1, - \frac{1}{10}, ...$ reason inductively that is., we can conclude based on past observations.

Observe that,

$\begin{matrix} 100 \times (- \frac{1}{10}) = - 10 \\ - 10 \times (- \frac{1}{10}) = 1 \\ 1 \times (- \frac{1}{10}) = - \frac{1}{10} \end{matrix}$

So, the pattern of the sequence is that the next term is $(- \frac{1}{10})$ times the previous term.

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

So, the next two term of the sequence will be $- \frac{1}{10} \times (- \frac{1}{10}) = \frac{1}{100}$ and $\frac{1}{100} \times (- \frac{1}{10}) = - \frac{1}{1000}$ .

Therefore, the sequence will be, $100, - 10, 1, - \frac{1}{10}, \underline{\frac{1}{100}}, \underline{- \frac{1}{1000}}, ...$ .

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Use inductive reasoning to predict the next two numbers in each sequence.
$100, - 10, 1, - \frac{1}{10}, ....$ .

Short Answer

Step by step solution

Step 1. Define inductive reasoning.

Step 2. Look for a pattern.

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

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Use inductive reasoning to predict the next two numbers in each sequence.100, −10, 1, −110, .....

Short Answer

Step by step solution

Step 1. Define inductive reasoning.

Step 2. Look for a pattern.

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

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Calculus

Discrete Mathematics

Statistics

Theoretical and Mathematical Physics

Pure Maths

Study anywhere. Anytime. Across all devices.

Use inductive reasoning to predict the next two numbers in each sequence.
$100, - 10, 1, - \frac{1}{10}, ....$ .