The number of line segments in the 100th pattern is equal to 201 line segments.
What is the pattern behind the construction of equillateral triangles?
Triangles are polygons with three sides of equal length, herein we find constructions elaborated with equilateral triangles, in which two new line segments are added when an equilateral triangle is so. Then, the number of line segments can be modelled after the following linear progression formula:
n = 3 + 2 · (n - 1)
Where n is the number of equilateral triangles in the pattern.
If we know that n = 100, then the number of line segments is:
n = 3 + 2 · (100 - 1)
n = 3 + 2 · 99
n = 3 + 198
n = 201
The number of line segments in the 100th pattern is equal to 201 line segments.
To learn more on arithmetic series: https://brainly.com/question/10396151
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