How many equal line segments are needed to make a row of 25 triangles

At first I was going to say 75 but then I realized that you could flip the triangles as you are making them so they would fit into each other. They still form a row so while one triangle would take 3 segments, two triangles would only take 5 segments, three triangles would take 7 and so on - (add 2 for each new triangle)

We could make a chart and continue all the way up to 25 triangles but there is a better way.

The formula for finding the nth term of an arithmetic sequence is:

an = a1 + (n - 1) d.

where d = the common difference (in this case 2 since the sequence goes 3,5,7, etc) and a1 represents the starting number (in this case 3 for a single triangle) n=the term you want to get to (in this case 25)

So

a (₂₅) = 3 + (25-1) 2

a (₂₅) = 3 + 24 (2) = 3 + 48 = 51

I made the chart anyway to see if I was correct. and 51 is correct.