Final answer:
The correct method to determine the total number of logs in 10 rows with each row having one less log than the one below is option c) 20 + 19 + 18 + ... + 11, which sums the number of logs in each row, representing an arithmetic progression.
Step-by-step explanation:
To determine the total number of logs in 10 rows when Alberto is stacking firewood with 20 logs on the bottom row and each subsequent row having 1 fewer log than the row below, we should look for a formula that represents the sum of an arithmetic sequence. The options given are:
- 20 * 9
- 10 * (10 + 1) / 2
- 20 + 19 + 18 + ... + 11
- 20 * 2^9
The correct way to determine the total number of logs in this scenario is option c) 20 + 19 + 18 + ... + 11. This is because it directly sums the decreasing number of logs in each row, representing an arithmetic sequence with a difference of -1 between each term. Option b) represents the sum of the first 10 natural numbers, which is not relevant to this question. Options a) and d) do not correspond to the sequence presented by the stacking of firewood.
The arithmetic sequence starts with 20 logs in the bottom row and decreases by 1 log in each row above. By the 10th row, there would be 20 - (10 - 1) = 11 logs. The sum of this sequence can be found using the formula for the sum of an arithmetic series 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 = 10, a1 = 20, and an = 11, so the sum S10 = 10/2 * (20 + 11) = 5 * 31 = 155.