Question

On a large piece of paper, Dana creates a "rectangular spiral" by drawing line segments of lengths, in cm, of 1, 1, 2, 2, 3, 3, 4, 4, .... as shown. Dana's pen runs out of ink after the total of all the lengths he has drawn is 3000cm. What is the length of the longest line segment that Dana draws?

(A) 38
(B) 39
(C) 54
(D) 55
(E) 30

Answer 1

All right, so we are going to have:
\[
\sum_{n=1}^N 2n=3000
\]And we wish to find \(N\) (our maximum length segment).

How would we go about doing this?

Answer 2

Uh...
2n+n-1=3000?

Answer 3

2(n-1)=3000*