How many line segments are used to form the nth term in the sequence of figures?

To understand why the number of line segments used to form the nth term in the sequence of figures is represented by the expression 6n−2, let’s break down the reasoning behind it.

In many geometric or sequential patterns, a sequence develops by adding a specific number of elements (in this case, line segments) as the term number increases. When constructing a sequence, each term's figure is often built upon the previous term, which influences the calculation of line segments.

For this particular sequence, if the figures depict some form of tessellation or polygon construction, you might find that for each additional term (increasing n), a consistent pattern emerges which adds or modifies a set number of segments. The expression 6n may imply that there are 6 line segments used for every complete figure as n increases. The subtraction of 2 could represent a fixed number of segments that may not be reused or may be internal to the structure of the first figure (like overlapped segments or those not counted in total).

Thus, as you form the nth term, the linear relationship of 6n represents how segments grow with each term, while the −2 adjusts for specific structural factors in your figures.

Recognizing such patterns is crucial in understanding how