A pile of logs has 28 logs in the bottom layer, 27 in the second layer, 26 in the third, and so on. The top layer contains 20 logs. Find the total number of logs in the pile.
A)212 logs
B)432 logs
C)217 logs
D)214 logs
E)216 logs

Question

Quizplus · Accepted Answer

The total number of logs can be found by summing the arithmetic series from 20 to 28. The formula for the sum of an arithmetic series is $S_n = \frac{n}{2}(a_1 + a_n)$, where $n$ is the number of terms, $a_1$ is the first term, and $a_n$ is the last term. Here, $n = 28 - 20 + 1 = 9$, $a_1 = 20$, and $a_n = 28$. Thus, $S_n = \frac{9}{2}(20 + 28) = \frac{9}{2}(48) = 216$.

A Pile of Logs Has 28 Logs in the Bottom