Several logs are stored in a pile with 32 logs on the bottom layer, 31 on the second layer, 30 on the third layer, and so on. If the top layer has one log, how many logs are in the pile?
A)527
B)528
C)496
D)512
E)none of the above

Question

Quizplus · Accepted Answer

The pile has logs in an arithmetic sequence with a common difference of -1. We need to find the sum of the first 32 terms of this sequence and add 1 for the top layer. We can use the formula for the sum of an arithmetic sequence:
S = (n/2)(a + l) where S is the sum, n is the number of terms, a is the first term, and l is the last term.

In this case, n = 32, a = 32, and l = 1. 
S = (32/2)(32 + 1) + 1
S = 16(33) + 1
S = 528
So, there are 528 logs in the pile.

Several Logs Are Stored in a Pile with 32 Logs