Question

In a pile of logs, each layer contains one more log than the layer above, and the top layer contains just one log. If there are 105 logs in the pile how many layers are there?

Answer 1

To find the number of layers in the pile of logs, use the formula for the sum of an arithmetic progression. The number of layers in the pile of logs is 14.

Step-by-step explanation:

To find the number of layers in the pile of logs, we can use the concept of arithmetic progression. The formula for the sum of an arithmetic progression is given by S = n/2 * (2a + (n-1)d), where S is the sum, n is the number of terms, a is the first term, and d is the common difference. In this case, the first term a is 1 and the common difference d is 1, as each layer contains one more log than the layer above.

We are given that the sum S is 105 logs. Substituting these values into the formula, we have 105 = n/2 * (2 + (n-1)*1). Simplifying this equation, we get n^2 + n - 210 = 0. Solving this quadratic equation, we find that n = 14 or n = -15. Since the number of layers cannot be negative, the number of layers in the pile of logs is 14.