Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 3: Q4 (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 term 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, sequence with next two numbers is 1, 4, 16, 64, 25¯, 36¯, .....

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!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Classify each pair of angles as alternate interior, same side interior or corresponding angles

and

Draw a diagram of a six-sided box by following the steps below.

Draw a six-sided top. Then draw Draw vertical edges.

An exact copy of the top directly edges dashed

below it. Make invisible

Name two coplanar segments that do not intersect and yet are not parallel.

If m∠1=xwhat are the measures of the other numbered angels?

Use two lines of notebook paper as parallel lines and draw any

transversal. Use a protractor to measure

Measure one pair of alternate interior angles. Repeat the experiment with another transversal. What appears to be true?
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Calculus

Read Explanation

Logic and Functions

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Geometry

Read Explanation

Discrete Mathematics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free