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? Write the steps to calculate the equation for the problem and state the number of layers.

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- anonymous

So for the topmost layer you have 6 logs, then you have 8, then 10 etc.
6 + (6+2) + (6+2+2)+...+(6+2(n-1)) = 4n + 110.
You have to find the sum of an arithmetic sequence with first term 6 and common difference 2 with n terms.
First term: 6, Last term: 2n+4.
Then substitute
Sum of sequence = 4n+110
and solve for n.

- anonymous

okay this would be 4 divided by 110?

- anonymous

=25n

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- anonymous

Sorry, what is 25n? Sum of sequence or?

- anonymous

no the answer

- anonymous

I'm really not sure how to do this

- anonymous

Okay, so how would you find the sum of an arithmetic series? Say, if I told you the first term was 6, the last was 14, and the common difference was 2. (6 + 8 + 10 + 12 + 14.) Apart from adding them up one by one.

- anonymous

Since the terms increased by the same amount each time, you could take the average and multiply it by the number of terms. The average would be (first term + last term)/2.

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