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.
