SOLUTION: A pile of logs contains 20 logs on the topmost layer and each lower layer contains one more log than the above layer. If there are 25 layers in the pile, how many logs are there in
Algebra ->
Sequences-and-series
-> SOLUTION: A pile of logs contains 20 logs on the topmost layer and each lower layer contains one more log than the above layer. If there are 25 layers in the pile, how many logs are there in
Log On
Question 1132502: A pile of logs contains 20 logs on the topmost layer and each lower layer contains one more log than the above layer. If there are 25 layers in the pile, how many logs are there in all? Answer by greenestamps(13200) (Show Source):
Each layer farther down contains 1 more log than the above layer; that means the 25th (last) layer contains 20+24 = 44 logs.
The total number of logs is then
20+21+22+...+43+44
Since this is an arithmetic sequence, the average number of logs in each layer is the average of the numbers in the first and last layers: (20+44)/2 = 32.
Then the total number of logs in the pile is the number of layers, times the average number of logs in each layer: 25*32 = 800.
