A stack of boxes has 9 rows. The bottom row has 44 boxes, and the top row has 12 boxes. Assuming that the sequence of numbers that gives the number of boxes in succeeding rows is arithmetic, how many boxes does the stack contain? The stack contains boxes.
Solution
Step 1 ：We are given a stack of boxes with 9 rows. The bottom row has 44 boxes, and the top row has 12 boxes. We are told that the sequence of numbers that gives the number of boxes in succeeding rows is arithmetic.
Step 2 ：We can find the total number of boxes in the stack by summing the arithmetic sequence. The formula for the sum of an arithmetic sequence is \(\frac{n}{2} * (a + l)\), where n is the number of terms, a is the first term, and l is the last term.
Step 3 ：In this case, n = 9 (the number of rows), a = 44 (the number of boxes in the bottom row), and l = 12 (the number of boxes in the top row).
Step 4 ：Substituting these values into the formula, we get \(\frac{9}{2} * (44 + 12)\).
Step 5 ：Solving this expression gives us a total of 252 boxes.
Step 6 ：Final Answer: The stack contains \(\boxed{252}\) boxes.
