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InvestigationRecursive Toothpick Patterns Name Period Date You will need: a box of toothpicks need: In this investigation you will learn to create and apply recursive sequences bymodeling them with.

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To make 1 square she uses 4 toothpicks; to make 2 squares she uses 7 toothpicks; to make 3 squares she uses 10 toothpicks. For each new square she needs a further 3 toothpicks. If she wants to make # squares she will need 3# + 1 toothpicks. So 9 squares needs (3 x 9) + 1 = 28 toothpicks.

One (of many) answers is T = 3n + 1. So the tenth design will have 3(10) + 1 or 31 toothpicks; the 100th design will have 301 toothpicks.

So, in the nth figure, there are n + n + (n + 1) toothpicks.

Therefore, there are 61 toothpicks in the 20th patterns .

The numbers of toothpicks in the successive stages, T(1),...,T(10), are 1, 3, 7, 11, 15, 23, 35, 43, 47, 55. in Table 1. These two sequences respectively form entries A139251 and A139250 in [8].

In geometry, the toothpick sequence is a sequence of 2-dimensional patterns which can be formed by repeatedly adding line segments ("toothpicks") to the previous pattern in the sequence.

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Form Packages
Adoption
Bankruptcy
Contractors
Divorce
Home Sales
Employment
Identity Theft
Incorporation
Landlord Tenant
Living Trust
Name Change
Personal Planning
Small Business
Wills & Estates
Packages A-Z
Form Categories
Affidavits
Bankruptcy
Bill of Sale
Corporate - LLC
Divorce
Employment
Identity Theft
Internet Technology
Landlord Tenant
Living Wills
Name Change
Power of Attorney
Real Estate
Small Estates
Wills
All Forms
Forms A-Z
Form Library
Customer Service
Terms of Service
DMCA Policy
About Us
Blog
Affiliates
Contact Us
Privacy Notice
Delete My Account
Site Map
All Forms
Search all Forms
Industries
Forms in Spanish
Localized Forms
Legal Guides
Real Estate Handbook
All Guides
Prepared for You
Notarize
Incorporation services
Our Customers
For Consumers
For Small Business
For Attorneys
Our Sites
US Legal Forms
USLegal
FormsPass
pdfFiller
signNow
airSlate workflows
DocHub
Instapage
Social Media
Call us now toll free:
1-877-389-0141
As seen in:
  • USA Today logo picture
  • CBC News logo picture
  • LA Times logo picture
  • The Washington Post logo picture
  • AP logo picture
  • Forbes logo picture
© Copyright 1997-2025
airSlate Legal Forms, Inc.
3720 Flowood Dr, Flowood, Mississippi 39232