Chapter 9.3, Problem 40E

Solution

To identify: How many tiles are used in the deck Pat designs a patio with a trapezoid shaped deck consisting of 16 rows of congruent slate tiles. The numbers of tiles in the rows form an arithmetic sequence. The first row contains 15 tiles and the last row contains 30 tiles.

There are $360$ tiles used in the deck.

Given information:

The given term is. $a_1=15,a_{16}=30\text{and}n=16$

Explanation:

Consider the given term

Formula for the sum of the first $nth$ term in an arithmetic sequence: $S_n=\frac{n}{2}\left(a_1+a_n\right)$

Put the value of $a_1=15,n=16\text{and}{a}_{16}=30$

  $\begin{array}{l}{S}_n=\frac{n}{2}\left(a_1+a_n\right)\\ S_n=\frac{16}{2}\left(`15+30\right)\\ S_n=8\left(45\right)\\ S_n=360\end{array}$

So, there are $360$ tiles used in the deck.