Final answer:
The total number of logs in a pile with 30 logs in the bottom layer and each subsequent layer having one log less down to one log at the top is calculated using the arithmetic series sum formula, resulting in 420 logs. Option is correct.
Step-by-step explanation:
The student is asking how many logs will be in a pyramid-shaped pile if there are 30 logs in the bottom layer, with each layer above having one less log than the layer below it down to one log at the top layer. This is a mathematics problem involving the sum of an arithmetic series.
To calculate the total number of logs, we can use the formula for the sum of the first n terms of an arithmetic sequence, which is given by Sn = n/2(a1 + an), where n is the number of terms, a1 is the first term, and an is the last term. In this case, n=30 (since the layers go from 30 down to 1), a1=30, and an=1. Plugging these values into the formula, we get Sn = 30/2(30 + 1) = 15 * 31, which is equal to 420.
Therefore, the correct answer is 420 logs.