marv_1 2 years ago 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.

1. jessica.17

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.

2. marv_1

okay this would be 4 divided by 110?

3. marv_1

=25n

4. jessica.17

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

5. marv_1

6. marv_1

I'm really not sure how to do this

7. jessica.17

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.

8. jessica.17

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.