Ryan is building a triangle sequence so that one triangle is added to the right each time, as shown below. How many matchsticks will he use for the nth figure and for the figure one before the nth? Click the icon to view the matchstick square figures. The nth figure will take matchsticks to build. (Type an expression using n as the variable. Simplify your answer.) The figure one before the nth figure will take matchsticks to build. (Type an expression using n as the variable. Simplify your answer.)
Ryan is building a triangle sequence so that one triangle is added to the right each time, as shown below. How many matchsticks will he use for the nth figure and for the figure one before the nth? Click the icon to view the matchstick square figures. The nth figure will take matchsticks to build. (Type an expression using n as the variable. Simplify your answer.) The figure one before the nth figure will take matchsticks to build. (Type an expression using n as the variable. Simplify your answer.)
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter11: Rational And Irrational Numbers
Section11.6: The Pythagorean Theorem
Problem 2CE
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Transcribed Image Text:**Polyhedral Chain Growth Visualization**
In this diagram, we see a series of progressively larger polyhedral chains represented in three stages, labeled from 1 to 3. Here’s a detailed explanation of each stage:
1. **Stage 1:** The diagram begins with a single polyhedral unit. It is composed of interconnected hexagons and triangles. The vertices are highlighted in pink, and the edges connecting these vertices are black.
2. **Stage 2:** This stage shows a chain with two interconnected polyhedral units. Each unit shares a vertex with the next. Both polyhedra retain the same structure as seen in Stage 1, but the total length of the chain is doubled.
3. **Stage 3:** In this final stage, the chain consists of three interconnected polyhedral units. Each subsequent polyhedron is added by sharing vertices in a similar manner to the previous stages, forming a longer chain.
Additional Controls:
- **Print Button:** Clicking this will allow users to print the current visualization for offline study or review.
- **Done Button:** Clicking this button closes the information window.
This diagram is useful for understanding the growth patterns of polyhedral chains, often applicable in fields such as chemistry and materials science.
![**Building a Matchstick Triangle Sequence**
Ryan is building a triangle sequence so that one triangle is added to the right each time, as shown below. How many matchsticks will he use for the nth figure and for the figure one before the nth?
*Note: Click the icon to view the matchstick square figures.*
---
**The nth figure:**
The nth figure will take [ ] matchsticks to build.
(Type an expression using n as the variable. Simplify your answer.)
**The figure one before the nth figure:**
The figure one before the nth figure will take [ ] matchsticks to build.
(Type an expression using n as the variable. Simplify your answer.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F893c97d9-09c7-4f3e-b188-bcf1f5d21bb1%2Fbe1160ee-b65e-450d-bb0d-af83c9c99518%2Fdi27pfr_processed.png&w=3840&q=75)
Transcribed Image Text:**Building a Matchstick Triangle Sequence**
Ryan is building a triangle sequence so that one triangle is added to the right each time, as shown below. How many matchsticks will he use for the nth figure and for the figure one before the nth?
*Note: Click the icon to view the matchstick square figures.*
---
**The nth figure:**
The nth figure will take [ ] matchsticks to build.
(Type an expression using n as the variable. Simplify your answer.)
**The figure one before the nth figure:**
The figure one before the nth figure will take [ ] matchsticks to build.
(Type an expression using n as the variable. Simplify your answer.)
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