A pile of logs has 38 logs in the bottom layer, 37 in the second layer, 36 in the third, and so on. The top layer contains 28 logs. Find the total number of logs in the pile.
A)363 logs
B)361 logs
C)726 logs
D)359 logs
E)365 logs

Question

Quizplus · Accepted Answer

This is a sum of an arithmetic series where the first term $a = 38$, the last term $l = 28$, and the common difference $d = -1$. The number of terms $n$ can be found by rearranging the formula for the nth term of an arithmetic sequence, $l = a + (n-1)d$, giving $n = \frac{l - a}{d} + 1$. Substituting the given values gives $n = \frac{28 - 38}{-1} + 1 = 11$. The sum of the series $S_n = \frac{n}{2}(a + l)$ then gives $S_n = \frac{11}{2}(38 + 28) = \frac{11}{2} \times 66 = 363$.

A Pile of Logs Has 38 Logs in the Bottom