Question

A wall is built in such a way that the top row contains one block, the next lower row contains 3blocks, the next lower row contains 5 blocks, and so on, increasing by two blocks in each row.How many rows high is the wall if the total number of blocks used is 900?

Answer 1

We have:

row 1 = 1

row 2 = 3

row 3 = 5

Then, the sequence is given by:

$a_{n=}2n-1$

Then, to determine the row with 900 blocks we use the following formula:

$S_n=n(\frac{a_1+a_n}{2})$

Where: Sn = 900, an = 2n-1 and a1 = 1

$900=n(\frac{1+2n-1}{2})$

And solve for n (the number of rows):

$\begin{gathered} 900=n(\frac{2n}{2}) \\ 900=n(n) \\ 900=n^2 \\ \sqrt[]{900}=n \\ n=30 \end{gathered}$

Answer: 30 rows