Let the number of items in the bottom row be the first term and the items in the top row be the last term in the sequence. Now we can write the endpoints of the sequence as: We know that each row in the pile has one more than the row above it. Therefore, the number of items from the bottom row to the top row forms an arithmetic sequence. Each term is one less than the previous term, this means our common difference is We can write the sequence fully as: In order to find the total number of items in the pile, we need to find the sum of the terms in this sequence. We can use a calculator to find the sum directly.
The number of items in the pile is