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jmc

counting and probability junior

Problem

Congruent segments are used to form equilateral triangles in this sequence so that each figure contains one more triangle than the preceding figure. Figure 3 of the sequence is made with seven congruent segments. How many congruent segments must be used to make Figure 25 of the sequence?

problem
Solution
It takes 2 additional segments to create an additional triangle after the first. Since Figure has triangles, Figure 25 has 25 triangles. It takes 3 segments to create the first triangle and segments to create the 24 additional triangles, for a total of segments.
Final answer
51