Which step in the construction of copying a line segment ensures that the new line segment has the same length as the original line segment

The second step ensures that the new line segment has the same length as the original segment.

Step-by-step explanation:

The steps to copy a line segment:

1. Move the compass center to point P.

2. Adjust the radius of the compass to the length of the original line segment (PQ).

3. Move the compass center to R.

4. Draw an arc that intersects the line to the right of R.

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for