Question

1. carlos is stacking crates of water bottles for a warehouse display. each level has 3 fewer crates than the level below it. the first (bottom) level has 30 crates.

a. write a function to represent the arithmetic sequence.
b. how many crates will there be on the tenth level?
equation: $a_n = \square$
$a_{10} = \square$

Explanation:

Part a:

Step1: Recall arithmetic sequence formula

The formula for the \(n\)-th term of an arithmetic sequence is \(a_n = a_1+(n - 1)d\), where \(a_1\) is the first term and \(d\) is the common difference.

Step2: Identify \(a_1\) and \(d\)

Here, \(a_1 = 30\) (the first level has 30 crates) and \(d=- 3\) (each level has 3 fewer crates, so the common difference is - 3).

Step3: Substitute into the formula

Substitute \(a_1 = 30\) and \(d=-3\) into \(a_n=a_1+(n - 1)d\).
\[

$$\begin{align*} a_n&=30+(n - 1)(-3)\\ &=30-3n + 3\\ &=33-3n \end{align*}$$

\]

Step1: Use the formula from part a

We have the formula \(a_n=33-3n\). We need to find \(a_{10}\), so we substitute \(n = 10\) into the formula.

Step2: Substitute \(n = 10\)

\[

$$\begin{align*} a_{10}&=33-3\times10\\ &=33 - 30\\ &=3 \end{align*}$$

\]

Answer:

\(a_n=33 - 3n\)

Part b: