Several logs are stored in a pile with 30 logs on the bottom layer,29 on the second layer,28 on the third layer,and so on.If the top layer has one log,how many logs are in the pile?
A)464
B)465
C)450
D)435
E)none of the above

Question

Several logs are stored in a pile with 30 logs on the bottom layer,29 on the second layer,28 on the third layer,and so on.If the top layer has one log,how many logs are in the pile? ​
A)464
B)465
C)450
D)435
E)none of the above

Quizplus · Accepted Answer

We can add up the number of logs on each layer using the formula for the sum of an arithmetic series: Sn = n/2(2a + (n-1)d), where Sn is the sum of n terms, a is the first term, and d is the common difference. Using this formula, we have:

S30 = 30/2(2(30) + (30-1)(-1)) = 15(60-29) = 465

Therefore, there are 465 logs in the pile.

Several Logs Are Stored in a Pile with 30 Logs