What about a pyramid with three rows?

Using letter numbers for the bottom row, we can write an expression for the top row.

Question

What about a pyramid with three rows? Using letter numbers for the bottom row, we can write an expression for the top row.

Homi · Accepted Answer

In this pyramid, the value in each block is the sum of the values in the two blocks directly below it.

Step 1 — Label the bottom row

Let us start with the bottom row of the pyramid. The problem tells us to use letter numbers for the bottom row. We can see from the diagram that the bottom row has three blocks. We label them from left to right as $a$ , $b$ , and $c$ .

Diagram 1

Step 2 — Calculate the second row

Now, we will find the values for the blocks in the second row from the bottom. Each block's value is the sum of the two blocks directly below it. The first block in the second row is above 'a' and 'b'.

$\text{First block (second row)} = a + b$

The second block in the second row is above 'b' and 'c'.

$\text{Second block (second row)} = b + c$

Diagram 2

Step 3 — Calculate the top row

Finally, we will find the value for the single block in the top row. This block is above the two blocks we just calculated in the second row. So, its value is the sum of $(a+b)$ and $(b+c)$ .

$\text{Top block} = (a+b) + (b+c)$

Step 4 — Simplify the expression

Let us simplify the expression for the top block by combining like terms. We remove the brackets and add the terms together.

$\text{Top block} = a + b + b + c$

$= a + (b+b) + c$

$= a + 2b + c$

$\boxed{a + 2b + c}$

Answer

The expression for the top row of a three-row pyramid with bottom row $a, b, c$ is $a + 2b + c$ .

Question 10

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