similar triangles theorem

[bananasbasket]

i know this tackles the similar triangles theorem, but i’m having quite a hard time looking for the ratio for me to plug values in an arithmetic/geometric sum sequence. here’s a pic of the original question and another for what i’ve come up with so far. please help me out, thank you.

 

[Dr.Peterson]

It looks like you have all you need, and in fact have done more work than you need.

The ratio of each red segment to the one before it is a constant, equal to the ratio AD₁:AB. Do you see that?

So that is the common ratio in a geometries series, and you can use the formula for the sum of such a series to answer the question.

 

[bananasbasket]

i

It looks like you have all you need, and in fact have done more work than you need.

The ratio of each red segment to the one before it is a constant, equal to the ratio AD₁:AB. Do you see that?

So that is the common ratio in a geometries series, and you can use the formula for the sum of such a series to answer the question.

sorry for the late reply, thanks a lot! i got an answer of 12, and it was correct according to our instructor.