Chapter 3: Q15. (page 108)

For each exercise, write the equation you think should come next. Check your prediction with a calculator.
$\begin{array}{l} 1 \times 9 + 2 = 11 \\ 12 \times 9 + 3 = 111 \\ 123 \times 9 + 4 = 1111 \end{array}$

Short Answer

Expert verified

The next equation must be $1234 \times 9 + 5 = 11111$ .

Step by step solution

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.

Step 2. Look for a pattern.

While looking for a pattern in the sequence

$\begin{array}{l} 1 \times 9 + 2 = 11 \\ 12 \times 9 + 3 = 111 \\ 123 \times 9 + 4 = 1111 \end{array}$

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

As,

$\begin{array}{r} 1 \to 12 \to 123 \\ 2 \to 3 \to 4 \\ 11 \to 111 \to 1111 \end{array}$

And 9 is fixed.

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

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

$\begin{array}{r} 1 \to 12 \to 123 \to \underline{1234} \\ 2 \to 3 \to 4 \to \underline{5} \\ 11 \to 111 \to 1111 \to \underline{11111} \end{array}$

Therefore, the next equation must be $1234 \times 9 + 5 = 11111$ .

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

For each exercise, write the equation you think should come next. Check your prediction with a calculator.
$\begin{array}{l} 1 \times 9 + 2 = 11 \\ 12 \times 9 + 3 = 111 \\ 123 \times 9 + 4 = 1111 \end{array}$

Short Answer

Step by step solution

Step 1. Define deductive and 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

Probability and Statistics

Mechanics Maths

Decision Maths

Geometry

Logic and Functions

Pure Maths

Study anywhere. Anytime. Across all devices.

For each exercise, write the equation you think should come next. Check your prediction with a calculator.1×9+2=1112×9+3=111123×9+4=1111

Short Answer

Step by step solution

Step 1. Define deductive and 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

Probability and Statistics

Mechanics Maths

Decision Maths

Geometry

Logic and Functions

Pure Maths

Study anywhere. Anytime. Across all devices.

For each exercise, write the equation you think should come next. Check your prediction with a calculator.
$\begin{array}{l} 1 \times 9 + 2 = 11 \\ 12 \times 9 + 3 = 111 \\ 123 \times 9 + 4 = 1111 \end{array}$