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MATH / Congruent segments are used to form equilateral triangles in this sequence so…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

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?

[asy]
draw((0,0)--(10,0)--(5,8.7)--cycle);
draw((15,0)--(25,0)--(30,8.7)--(20,8.7)--cycle);
draw((20,8.7)--(25,0));
draw((35,0)--(55,0)--(50,8.7)--(40,8.7)--cycle);
draw((40,8.7)--(45,0)--(50,8.7));
draw((60,0)--(80,0)--(85,8.7)--(65,8.7)--cycle);
draw((65,8.7)--(70,0)--(75,8.7)--(80,0));
label("Figure 1",(2,0),S);
label("Figure 2",(20,-10),S);
label("Figure 3",(45,0),S);
label("Figure 4",(76,-10),S);
[/asy]

level

Level 2

type

Counting & Probability

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Source and history

task_id
796e7416-d2a2-5195-b3c0-dd3e9cccfc30
task_key
counting~5fand~5fprobability--test--796e7416-d2a2-5195-b3c0-dd3e9cccfc30
task_revision_id
1
config / split
counting_and_probability / test

Official source

initial import