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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
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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)
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