# Thread: Geometrical sequence word problem help..

1. ## Geometrical sequence word problem help..

A beetle starts at a point O on the floor. It walks 1m east, then 1/2m west, then 1/4m east and so on. How far it finish off O and how far did it actually walk?

Now here's my working:

We are given, ratio r = -(1/2), and first term a = 1 ... Since |r| < 1, it's a series that converges to a limit, so:

S = a / 1 - r
S = 1 / 1 - (-1/2) = 2/3

Therefore, the beetle ends up 2/3m from O.

Now ... I want help with how far did it actually walk. How should I go about calculating that?

2. The total distance walked is given by the infinite series:

$\displaystyle d=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}\cdots$

since distance has no sense of direction, only magnitude. Does this help?

3. Originally Posted by Greengoblin
The total distance walked is given by the infinite series:

$\displaystyle d=1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}\cdots$

since distance has no sense of direction, only magnitude. Does this help?
Thanks but how to calculate how long this series continue until?

4. Originally Posted by struck
Thanks but how to calculate how long this series continue until?
It's an infinite geometric series. $\displaystyle S = \frac{a}{1 - r}$ where r = 1/2.