A pile of logs has 34 logs in the bottom layer, 32 in the second layer, 30 in the third, and so on. The top layer contains 12 logs. Find the total number of logs in the pile.
A)276 logs
B)270 logs
C)552 logs
D)274 logs
E)272 logs

Question

Quizplus · Accepted Answer

The number of logs forms an arithmetic sequence with the first term 34 and the last term 12, with a common difference of -2. The number of terms can be found using the formula for the nth term of an arithmetic sequence: 12 = 34 + (n-1)(-2). Solving gives n = 12. The sum of the sequence is given by the formula S = n/2 * (first term + last term) = 12/2 * (34 + 12) = 276 logs.

A Pile of Logs Has 34 Logs in the Bottom