Question

debra made a pattern of equilateral triangles using toothpicks. she recorded the, pattern, number of triangles, and number of toothpicks in a table. fill in the missing value in the table. then use the rule to predict the number of toothpicks for 17 triangles. in the pattern with 17 triangles, there will be toothpicks.

Explanation:

Step1: Find the pattern rule

Let \(n\) be the number of triangles. When \(n = 1\), the number of tooth - picks \(y=3=2\times1 + 1\); when \(n = 2\), \(y = 5=2\times2+1\). So the rule is \(y = 2n+1\).

Step2: Calculate the number of tooth - picks for \(n = 3\)

Substitute \(n = 3\) into the formula \(y=2n + 1\). Then \(y=2\times3+1=6 + 1=7\).

Step3: Calculate the number of tooth - picks for \(n = 17\)

Substitute \(n = 17\) into the formula \(y=2n+1\). Then \(y=2\times17+1=34 + 1=35\).

Answer:

The missing value (for \(3\) triangles) is \(7\). For \(17\) triangles, there will be \(35\) tooth - picks.