Math Is Fun Forum

chetah

Member

Registered: 2008-02-15

Posts: 32

Discret Math

A lumberjack has 4n + 110 logs in a pile consisting of n layers.  Each layer has two more logs than the layer directly above it.  If the top layer has six logs, how many layers are there?

My solution n = 55

Daniel123

Member

Registered: 2007-05-23

Posts: 663

Re: Discret Math

I get 10.

The logs in each layer form an arithmetic series with first term 6, common difference 2 and number of terms n.

The sum of an arithmetic sequence is given by

If we evaluate this sum:

However, the question tell us that there are 4n + 110 logs. Therefore we know that:

Which gives n = 10.

I think you have forgotten to add the extra two logs for each layer; your answer implies there are 330 logs, and 6 x 55 = 330.

Last edited by Daniel123 (2008-03-31 02:06:30)