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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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This guide provides step-by-step instructions for completing the Investigation Recursive Toothpick Patterns Investigation form online. Follow these detailed instructions to ensure a smooth and successful submission.

Follow the steps to complete the online form effectively.

  1. Press the ‘Get Form’ button to obtain the Investigation Recursive Toothpick Patterns Investigation form and open it in your preferred online editor.
  2. Enter your name in the designated field. This ensures that your submission is correctly attributed to you.
  3. Next, fill in the period and date fields to provide context for your investigation.
  4. In the section concerning the activities, outline the materials needed, including the box of toothpicks.
  5. Proceed to fill out each step of the investigation as per the instructions provided in the document. Document your findings for each figure regarding the number of toothpicks used and the perimeter, as indicated.
  6. In subsequent sections, write the rules you discovered for finding the number of toothpicks and the perimeter for different figures in the designated fields.
  7. If applicable, repeat the design process and calculations for the new pattern using squares, recording your results in the provided table.
  8. Finally, review all the entered information, ensuring accuracy before saving your changes or downloading a copy of the completed document.

Complete your Investigation Recursive Toothpick Patterns Investigation online today for a seamless experience.

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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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