Questions.

[dekoyl]

I will post a few questions here before I have my exams. I hope there are enough people remaining to help me out. Thanks 

1.An equilateral triangle as perimeter p. The midpoints of the sides are joined to form another triangle, and this process is repeated.
Find: *the perimeter and the area of the triangle.
        *the limits as of the sums of perimeters and areas of the first n triangles

2.The fourth, seventh and sixteenth terms of an arithmetic sequence also form consecutive terms of geometric sequence. Find the common ratio of the geometric sequence.

I get stuck with this one. Not even sure if I'm using the right method.







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[/0]

1.

Part a)

Draw a diagram. For example, I have used the triforce to illustrate the first step.



As you can see, if the side length of the larger triangle is , then the side length of the smaller triangle is .

Perimeter:
The perimeter of the larger triangle is , and the perimeter of the smaller triangle is .

Taking the largest triangle to be the 1st triangle, we have a geometric series with ,



Area:
The area of the larger triangle is (several ways of doing this, fastest probably using )

And the area of the smaller triangle

This is also geometric, with and (this is, by no coincidence, the square of the ratio of perimeter change).



Part b)

For the perimeter:

For the area:


2. You're on the right track













Assmuing ,









This problem shows that when you don't know how to do something, test different things out, even if they seem unlikely. Normally when you see simultaneous equations you would solve by substitution. Even though this had 3 variables in 2 equations, using substitution it eventually came out with an answer
good luck with your exam

[dekoyl]

Zelda reference?

Thanks /0!