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((a_1+a_n)/(2))`

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

`900=n((1+2n-1)/(2))`

And solve for n (the number of rows):

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

Answer: 30 rows