Mathematics

Problem

A builder is arranging bricks in horizontal rows to form a triangular stack. The bottom row contains 50 bricks, the next row contains 49 bricks, the row above it contains 48 bricks, and so on, with each higher row having one brick fewer than the row just below it. The topmost row ends with exactly 10 bricks. a. (i) Determine the total number of rows in the stack. b. (ii) Calculate the total number of bricks used to build the entire stack. c. (iii) If each brick weighs 2 kg, find the total weight of the stack in kilograms.

Intuitive explanation

This is an arithmetic series problem where you need to find the total count across all rows. The key insight is recognizing that the rows form a sequence: 50, 49, 48, ..., 10—each decreasing by 1. Rather than adding all these individually, use the arithmetic series formula $S = \frac{n(a_1 + a_n)}{2}$ , where $n$ is the number of terms, $a_1$ is the first term, and $a_n$ is the last term. First, count how many rows exist, then apply the formula to find the total bricks.

Intuitive explanation

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