Explanation Given information: The numbers x , y , and z are in a Fibonacci sequence and z = x + y . Calculation: In an arithmetic sequence, difference between any two consecutive terms is constant. Consider, x , y , and z that makes an arithmetic sequence as well as consecutive terms. Thus, y − x = z − y . By simplifying, 2 y = x + z But given that, z = x + y ⇒ 2 y = x + x + y ⇒ 2 y = 2 x + y ⇒ y = 2 x Thus, y = 2 x

Problem Solving Approach to Mathematics for Elementary School Teachers, A, Plus MyLab Math -- Access Card Package (12th Edition)

12th Edition

ISBN: 9780321990594

Author: Rick Billstein, Shlomo Libeskind, Johnny Lott

Publisher: PEARSON

See similar textbooks

Concept explainers

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence. It was invented by German mathematician Carl Friedrich Gauss.

Videos

Question

Chapter 1.2, Problem 5MC

To determine

All triples x, y, and z that make an arithmetic sequence as well as consecutive terms in a Fibonacci-type sequence, if x, y, and z are in a Fibonacci sequence and z=x+y by using deductive reasoning.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 1.2, Problem 4MC

Chapter 1.2, Problem 6MC

Students have asked these similar questions

question 8

Two construction companies are bidding against one another for the right to construct a new community center building. The first construction company, Fine Line Homes, believes that its competitor, Buffalo Valley Construction, will place a bid for this project according to the distribution shown in this table: Buffalo Valley's Bid Bid Probability $160,000 0.2 $165,000 0.5 $170,000 0.2 $175,000 0.1 Furthermore, Fine Line Homes estimates that it will cost $160,000 for its own company to construct this building. Given its fine reputation and long-standing service within the local community, Fine Line Homes believes that it will likely be awarded the project in the event that it and Buffalo Valley Construction submit exactly the same bids. Find the bid that maximizes Fine Line’s expected profit. Max expected profit $ ________ . Bid that maximizes profit $ ________ .

Find the area of the surface obtained by rotating the circle x² + y² = r² about the line y = r.

Chapter 1 Solutions

Problem Solving Approach to Mathematics for Elementary School Teachers, A, Plus MyLab Math -- Access Card Package (12th Edition)

Ch. 1.1 - Mathematical Connections 1-2 a. If a fixed number...Ch. 1.1 - Mathematical Connections 1-2 A student says she...Ch. 1.1 - Mathematical Connections 1-2 Abby and Dan are...Ch. 1.1 - Consider a game where you have two distict piles...Ch. 1.1 - Mathematical Connections 1-2 A mathematician named...Ch. 1.1 - Mathematical Connections 1-2 The figure below...Ch. 1.1 - Mathematical Connections 1-1 The distance around...Ch. 1.1 - Work in pairs on the following versions of a game...Ch. 1.1 - John asks why the last step of Polyas four-step...Ch. 1.1 - Mathematical Connections 1-2 Connecting...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.

All triples x , y , and z that make an arithmetic sequence as well as consecutive terms in a Fibonacci-type sequence, if x , y , and z are in a Fibonacci sequence and z = x + y by using deductive reasoning.

Solution Summary: The author explains that the triples that make an arithmetic sequence as well as consecutive terms is constant.

Concept explainers

Videos

All triples x, y, and z that make an arithmetic sequence as well as consecutive terms in a Fibonacci-type sequence, if x, y, and z are in a Fibonacci sequence and z=x+y by using deductive reasoning.

Want to see the full answer?

Chapter 1 Solutions