SOLUTION: logs are stacked in a pile with 24 logs on the bottom row and 15 on the top row. there are 10 rows in all with each row having one more log than the one above it. how many logs are
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Question 1206889: logs are stacked in a pile with 24 logs on the bottom row and 15 on the top row. there are 10 rows in all with each row having one more log than the one above it. how many logs are in the stack
The 10 rows have numbers of logs that form an arithmetic sequence.
With 10 rows and 24 on the bottom row and 15 on the top row, the common difference in the arithmetic sequence is 1.
But we don't need to know that common difference to answer the question.
In any set of numbers, the sum of the numbers is
(number of numbers) * (average of the numbers)
In an arithmetic sequence, the average of all the numbers is the average of the first and last numbers.
In this problem we are given the number of rows of logs and the numbers of logs in the first and last rows, so we have all we need to find the total number of logs.
logs are stacked in a pile with 24 logs on the bottom row and 15 on the top row. there are 10 rows in all with each row having one more log than the one above it. how many logs are in the stack
This problem involves the SUM of an AP (Arithmetic Progression)/AS (Arithmetic Sequence), and is
denoted by the following formula: , where:
= Sum of the AP/AS (UNKNOWN, in this case).
= Number of terms/rows (10, in this case).
= First term/row (15, in this case).
= Last term/row (24, in this case).
now becomes:
Sum of this AP/AS, or
